From b0bdc9d8ba69bfbf2693efade48770fbf3cedef7 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Mon, 25 Aug 2025 17:13:18 +0200
Subject: [PATCH 01/25] custom `(left/right)oneunit` and `blocksectors` for
 `SumSpace` of `IsingBimodule` spaces

---
 src/vectorspaces/multifusionsumspace.jl | 39 +++++++++++++++++++++++++
 1 file changed, 39 insertions(+)
 create mode 100644 src/vectorspaces/multifusionsumspace.jl

diff --git a/src/vectorspaces/multifusionsumspace.jl b/src/vectorspaces/multifusionsumspace.jl
new file mode 100644
index 0000000..f580662
--- /dev/null
+++ b/src/vectorspaces/multifusionsumspace.jl
@@ -0,0 +1,39 @@
+# custom methods for SumSpaces
+
+function Base.oneunit(S::SumSpace{Vect[IsingBimodule]})
+    @assert !isempty(S) "Cannot determine type of empty space"
+    allequal(a.row for a in sectors(S)) && allequal(a.col for a in sectors(S)) ||
+        throw(ArgumentError("sectors of $S are not all equal"))
+    first(sectors(S)).row == first(sectors(S)).col || throw(ArgumentError("non-diagonal SumSpace $S"))
+    return SumSpace(oneunit(first(S.spaces)))
+end
+
+function TensorKit.rightoneunit(S::SumSpace{Vect[IsingBimodule]})
+    @assert !isempty(S) "Cannot determine type of empty space"
+    allequal(a.col for a in sectors(S)) || throw(ArgumentError("sectors of $S do not have the same rightone"))
+    return SumSpace(TensorKit.rightoneunit(first(S.spaces)))
+end
+
+function TensorKit.leftoneunit(S::SumSpace{Vect[IsingBimodule]})
+    @assert !isempty(S) "Cannot determine type of empty space"
+    allequal(a.row for a in sectors(S)) || throw(ArgumentError("sectors of $S do not have the same leftone"))
+    return SumSpace(TensorKit.leftoneunit(first(S.spaces)))
+end
+
+function TensorKit.blocksectors(W::TensorMapSpace{SumSpace{Vect[IsingBimodule]},N₁,N₂}) where {N₁,N₂}
+    codom = codomain(W)
+    dom = domain(W)
+    if N₁ == 0 && N₂ == 0
+        return (IsingBimodule(1, 1, 0), IsingBimodule(2, 2, 0)) # should this be a vector?
+    elseif N₁ == 0
+        @assert N₂ != 0 "one of Type IsingBimodule doesn't exist"
+        return filter!(isone, collect(blocksectors(dom)))
+    elseif N₂ == 0
+        @assert N₁ != 0 "one of Type IsingBimodule doesn't exist"
+        return filter!(isone, collect(blocksectors(codom)))
+    elseif N₂ <= N₁ # keep intersection
+        return filter!(c -> TK.hasblock(codom, c), collect(blocksectors(dom)))
+    else
+        return filter!(c -> TK.hasblock(dom, c), collect(blocksectors(codom)))
+    end
+end
\ No newline at end of file

From e5bb078491def9882654673252077779886774ea Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Mon, 25 Aug 2025 17:13:59 +0200
Subject: [PATCH 02/25] start of `IsingBimodule` `SumSpace` tests

---
 test/vectorspaces/sumspace.jl | 68 ++++++++++++++++++++++++++++++++++-
 1 file changed, 67 insertions(+), 1 deletion(-)

diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index 1f6524d..aec140d 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -103,7 +103,7 @@ end
     @test !(V ≻ ⊕(V, V))
 end
 
-@testset"GradedSpace" begin
+@testset "GradedSpace" begin
     using TensorKit, BlockTensorKit
     using Test, TestExtras
 
@@ -156,3 +156,69 @@ end
     @test V ≺ ⊕(V, V)
     @test !(V ≻ ⊕(V, V))
 end
+
+@testset "MultFusion" begin
+    using TensorKit, BlockTensorKit
+    using Test, TestExtras
+
+    using TensorKit: hassector
+    using BlockTensorKit: ⊕
+
+    I = IsingBimodule
+
+    C0, C1, D0, D1, M, Mop = I(1, 1, 0), I(1, 1, 1), I(2, 2, 0), I(2, 2, 1), I(1, 2, 0), I(2, 1, 0)
+
+    V1 = Vect[I](C0 => 1, C1 => 1)
+    V2 = Vect[I](D0 => 1, D1 => 1)
+    V3 = Vect[I](M => 1) # no Mop
+    d = dim(V1) + dim(V2) + dim(V3)
+    V = SumSpace(V1, V2, V3)
+
+    @test isa(V, VectorSpace)
+    @test isa(V, ElementarySpace)
+
+    @test isa(InnerProductStyle(V), HasInnerProduct)
+    @test isa(InnerProductStyle(V), EuclideanInnerProduct)
+    @test isa(V, SumSpace)
+
+    @test !isdual(V)
+    @test isdual(V')
+
+    @test @constinferred(hash(V)) == hash(deepcopy(V))
+    @test @constinferred(dual(V)) == @constinferred(conj(V)) == @constinferred(adjoint(V))
+    @test field(V) == ℂ
+
+    @test_throws ArgumentError("one of Type IsingBimodule doesn't exist") oneunit(V)
+    # TODO: get left/rightoneunit working
+
+    @test @constinferred(sectortype(V)) == sectortype(V1)
+    @test ((@constinferred sectors(V))...,) == (C1, C0, D1, D0, M) # why does ordering matter?
+    @test length(sectors(V)) == 5
+    @test @constinferred(hassector(V, M))
+    @test !@constinferred(hassector(V, Mop))
+    @test @constinferred(dim(V)) ==
+        d ==
+        @constinferred(sum(dim(s) for s in sectors(V)))
+    @test dim(@constinferred(typeof(V)())) == 0
+    @test (sectors(typeof(V)())...,) == ()
+
+    W = @constinferred SumSpace(Vect[I](M => 1))
+    @test @constinferred(oneunit(V)) == W == @constinferred(oneunit(typeof(V)))
+
+    VC = SumSpace(V1, V1) # TODO: finish tests with these
+    VCM = SumSpace(V1, V3)
+    VMD = SumSpace(V2, V3)
+
+    @test @constinferred(⊕(V, V)) == SumSpace(vcat(V.spaces, V.spaces))
+    @test @constinferred(⊕(V, oneunit(V))) == SumSpace(vcat(V.spaces, oneunit(V1)))
+    @test @constinferred(⊕(V, V, V, V)) == SumSpace(repeat(V.spaces, 4))
+    @test @constinferred(fuse(VC, VC)) ≅ SumSpace(Vect[I](C0 => 8, C1 => 8))
+    @test @constinferred(fuse(VC, VC', VC, VC')) ≅
+        SumSpace(Vect[I](C0 => 128, C1 => 128))
+    @test @constinferred(flip(V)) ≅ SumSpace(flip.(V.spaces)...)
+    @test flip(V) ≅ V
+    @test flip(V) ≾ V
+    @test flip(V) ≿ V
+    @test V ≺ ⊕(V, V)
+    @test !(V ≻ ⊕(V, V))
+end
\ No newline at end of file

From 84b5ef618d116ad1c1cec9366501794c16ed5dbb Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Mon, 25 Aug 2025 17:14:07 +0200
Subject: [PATCH 03/25] import `hasblock`

---
 src/BlockTensorKit.jl | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/BlockTensorKit.jl b/src/BlockTensorKit.jl
index bdc4042..fc7e82b 100644
--- a/src/BlockTensorKit.jl
+++ b/src/BlockTensorKit.jl
@@ -23,7 +23,8 @@ using TensorKit:
     AdjointTensorMap,
     adjointtensorindices,
     compose,
-    sectorscalartype
+    sectorscalartype,
+    hasblock
 using VectorInterface
 using TensorOperations
 using TensorOperations:
@@ -52,6 +53,7 @@ import TupleTools as TT
 # Spaces
 include("vectorspaces/sumspace.jl")
 include("vectorspaces/sumspaceindices.jl")
+include("vectorspaces/multifusionsumspace.jl")
 
 # Tensors
 include("tensors/abstractblocktensor/abstractblocktensor.jl")

From ed522adf8bfc24ef904996652dc5b9e74a5f12b4 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 26 Aug 2025 09:23:43 +0200
Subject: [PATCH 04/25] finish multifusion tests

---
 test/vectorspaces/sumspace.jl | 44 ++++++++++++++++++++++++++++-------
 1 file changed, 35 insertions(+), 9 deletions(-)

diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index aec140d..856fb0f 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -157,7 +157,7 @@ end
     @test !(V ≻ ⊕(V, V))
 end
 
-@testset "MultFusion" begin
+@testset "Multifusion" begin
     using TensorKit, BlockTensorKit
     using Test, TestExtras
 
@@ -188,11 +188,10 @@ end
     @test @constinferred(dual(V)) == @constinferred(conj(V)) == @constinferred(adjoint(V))
     @test field(V) == ℂ
 
-    @test_throws ArgumentError("one of Type IsingBimodule doesn't exist") oneunit(V)
-    # TODO: get left/rightoneunit working
+    @test_throws ArgumentError("sectors of $V are not all equal") oneunit(V)
 
     @test @constinferred(sectortype(V)) == sectortype(V1)
-    @test ((@constinferred sectors(V))...,) == (C1, C0, D1, D0, M) # why does ordering matter?
+    @test ((@constinferred sectors(V))...,) == (C1, C0, D1, D0, M) # ordering matters
     @test length(sectors(V)) == 5
     @test @constinferred(hassector(V, M))
     @test !@constinferred(hassector(V, Mop))
@@ -202,15 +201,30 @@ end
     @test dim(@constinferred(typeof(V)())) == 0
     @test (sectors(typeof(V)())...,) == ()
 
-    W = @constinferred SumSpace(Vect[I](M => 1))
-    @test @constinferred(oneunit(V)) == W == @constinferred(oneunit(typeof(V)))
-
-    VC = SumSpace(V1, V1) # TODO: finish tests with these
+    # (left/right)oneunit tests
+    WC = @constinferred SumSpace(Vect[I](C0 => 1))
+    WD = @constinferred SumSpace(Vect[I](D0 => 1))
+    WM = @constinferred SumSpace(V3)
+    WMop = @constinferred SumSpace(Vect[I](Mop => 1))
+    for W in [WC, WD]
+        @test @constinferred(oneunit(W)) == W == @constinferred(leftoneunit(W)) == @constinferred(rightoneunit(W))
+        @test_throws ArgumentError("one of Type IsingBimodule doesn't exist") oneunit(typeof(W))
+    end
+
+    @test leftoneunit(WMop) == WD && rightoneunit(WMop) == WC
+    @test leftoneunit(WM) == WC && rightoneunit(WM) == WD
+    @test_throws ArgumentError("non-diagonal SumSpace $WM") oneunit(WM)
+    @test_throws ArgumentError("non-diagonal SumSpace $WMop") oneunit(WMop)
+
+    VC = SumSpace(V1, V1)
     VCM = SumSpace(V1, V3)
     VMD = SumSpace(V2, V3)
 
     @test @constinferred(⊕(V, V)) == SumSpace(vcat(V.spaces, V.spaces))
-    @test @constinferred(⊕(V, oneunit(V))) == SumSpace(vcat(V.spaces, oneunit(V1)))
+    @test @constinferred(⊕(VC, oneunit(VC))) == SumSpace(vcat(VC.spaces, oneunit(VC)))
+    @test @constinferred(⊕(VCM, leftoneunit(VCM))) == SumSpace(vcat(VCM.spaces, leftoneunit(VCM)))
+    @test @constinferred(⊕(VMD, rightoneunit(VMD))) == SumSpace(vcat(VMD.spaces, rightoneunit(VMD)))
+
     @test @constinferred(⊕(V, V, V, V)) == SumSpace(repeat(V.spaces, 4))
     @test @constinferred(fuse(VC, VC)) ≅ SumSpace(Vect[I](C0 => 8, C1 => 8))
     @test @constinferred(fuse(VC, VC', VC, VC')) ≅
@@ -221,4 +235,16 @@ end
     @test flip(V) ≿ V
     @test V ≺ ⊕(V, V)
     @test !(V ≻ ⊕(V, V))
+
+    # blocksectors tests
+    @test @constinferred(blocksectors(one(V) ← one(V))) == [C0, D0]
+    @test @constinferred(blocksectors(V ← V)) == sort(collect(sectors(V))) # convert set to vector
+    @test @constinferred(blocksectors(one(V))) == [C0, D0]
+    for v in [VC, VCM, VMD]
+        @test @constinferred(blocksectors(v^2)) == blocksectors(v ← v)
+    end
+    for v in [WM, WMop]
+        @test isempty(@constinferred(blocksectors(v^2)))
+        @test @constinferred(blocksectors(v ← v)) == blocksectors(v)
+    end
 end
\ No newline at end of file

From f033921cc26d2f4f3323f167627e48a1981031f9 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 26 Aug 2025 09:24:33 +0200
Subject: [PATCH 05/25] add `blocksectors` for `ProductSpace` for
 `IsingBimodule`

---
 src/vectorspaces/multifusionsumspace.jl | 23 ++++++++++++++++++++++-
 1 file changed, 22 insertions(+), 1 deletion(-)

diff --git a/src/vectorspaces/multifusionsumspace.jl b/src/vectorspaces/multifusionsumspace.jl
index f580662..93f732b 100644
--- a/src/vectorspaces/multifusionsumspace.jl
+++ b/src/vectorspaces/multifusionsumspace.jl
@@ -24,7 +24,7 @@ function TensorKit.blocksectors(W::TensorMapSpace{SumSpace{Vect[IsingBimodule]},
     codom = codomain(W)
     dom = domain(W)
     if N₁ == 0 && N₂ == 0
-        return (IsingBimodule(1, 1, 0), IsingBimodule(2, 2, 0)) # should this be a vector?
+        return [IsingBimodule(1, 1, 0), IsingBimodule(2, 2, 0)]
     elseif N₁ == 0
         @assert N₂ != 0 "one of Type IsingBimodule doesn't exist"
         return filter!(isone, collect(blocksectors(dom)))
@@ -36,4 +36,25 @@ function TensorKit.blocksectors(W::TensorMapSpace{SumSpace{Vect[IsingBimodule]},
     else
         return filter!(c -> TK.hasblock(dom, c), collect(blocksectors(codom)))
     end
+end
+
+function TensorKit.blocksectors(P::ProductSpace{SumSpace{Vect[IsingBimodule]},N}) where {N}
+    I = sectortype(P) # IsingBimodule
+    bs = Vector{I}()
+    if N == 0
+        return [IsingBimodule(1, 1, 0), IsingBimodule(2, 2, 0)]
+    elseif N == 1
+        for s in sectors(P)
+            push!(bs, first(s))
+        end
+    else
+        for s in sectors(P)
+            for c in ⊗(s...)
+                if !(c in bs)
+                    push!(bs, c)
+                end
+            end
+        end
+    end
+    return sort!(bs)
 end
\ No newline at end of file

From 36f6413469a2c99538fb6eee523223b9c009867e Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 26 Aug 2025 10:01:17 +0200
Subject: [PATCH 06/25] `left/rightoneunit` for `SumSpace` of `GradedSpace` +
 test

---
 src/vectorspaces/sumspace.jl  | 8 ++++++++
 test/vectorspaces/sumspace.jl | 1 +
 2 files changed, 9 insertions(+)

diff --git a/src/vectorspaces/sumspace.jl b/src/vectorspaces/sumspace.jl
index 21bf105..4b84541 100644
--- a/src/vectorspaces/sumspace.jl
+++ b/src/vectorspaces/sumspace.jl
@@ -152,6 +152,14 @@ end
 
 Base.oneunit(S::Type{<:SumSpace}) = SumSpace(oneunit(eltype(S)))
 
+function TensorKit.leftoneunit(S::SumSpace{<:GradedSpace})
+    return SumSpace(leftoneunit(first(S)))
+end
+
+function TensorKit.rightoneunit(S::SumSpace{<:GradedSpace})
+    return SumSpace(rightoneunit(first(S)))
+end
+
 # Promotion and conversion
 # ------------------------
 Base.promote_rule(::Type{S}, ::Type{SumSpace{S}}) where {S <: ElementarySpace} = SumSpace{S}
diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index 856fb0f..3ceb7eb 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -143,6 +143,7 @@ end
     @test @constinferred(axes(V)) == Base.OneTo(d)
     W = @constinferred SumSpace(U1Space(0 => 1))
     @test @constinferred(oneunit(V)) == W == @constinferred(oneunit(typeof(V)))
+    @test @constinferred(leftoneunit(V)) == W == @constinferred(rightoneunit(V))
     @test @constinferred(⊕(V, V)) == SumSpace(vcat(V.spaces, V.spaces))
     @test @constinferred(⊕(V, oneunit(V))) == SumSpace(vcat(V.spaces, oneunit(V1)))
     @test @constinferred(⊕(V, V, V, V)) == SumSpace(repeat(V.spaces, 4))

From 70e0cccfbfa8acf0081f83ec77f3698469b4cf19 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 26 Aug 2025 11:50:08 +0200
Subject: [PATCH 07/25] redefine `left/rightoneunit` for usual `GradedSpace`s

---
 src/vectorspaces/sumspace.jl | 8 ++------
 1 file changed, 2 insertions(+), 6 deletions(-)

diff --git a/src/vectorspaces/sumspace.jl b/src/vectorspaces/sumspace.jl
index 4b84541..0c20f03 100644
--- a/src/vectorspaces/sumspace.jl
+++ b/src/vectorspaces/sumspace.jl
@@ -152,13 +152,9 @@ end
 
 Base.oneunit(S::Type{<:SumSpace}) = SumSpace(oneunit(eltype(S)))
 
-function TensorKit.leftoneunit(S::SumSpace{<:GradedSpace})
-    return SumSpace(leftoneunit(first(S)))
-end
+TensorKit.leftoneunit(S::SumSpace{<:GradedSpace}) = SumSpace(leftoneunit(first(S)))
 
-function TensorKit.rightoneunit(S::SumSpace{<:GradedSpace})
-    return SumSpace(rightoneunit(first(S)))
-end
+TensorKit.rightoneunit(S::SumSpace{<:GradedSpace}) = SumSpace(rightoneunit(first(S)))
 
 # Promotion and conversion
 # ------------------------

From 76184b65178861a86612b982cdbc27f747b32b63 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 26 Aug 2025 11:51:11 +0200
Subject: [PATCH 08/25] extra check to `IsingBimodule` `SumSpace`s when empty

---
 src/vectorspaces/multifusionsumspace.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/vectorspaces/multifusionsumspace.jl b/src/vectorspaces/multifusionsumspace.jl
index 93f732b..0bd17e6 100644
--- a/src/vectorspaces/multifusionsumspace.jl
+++ b/src/vectorspaces/multifusionsumspace.jl
@@ -1,7 +1,7 @@
 # custom methods for SumSpaces
 
 function Base.oneunit(S::SumSpace{Vect[IsingBimodule]})
-    @assert !isempty(S) "Cannot determine type of empty space"
+    @assert !isempty(sectors(S)) "Cannot determine type of empty space"
     allequal(a.row for a in sectors(S)) && allequal(a.col for a in sectors(S)) ||
         throw(ArgumentError("sectors of $S are not all equal"))
     first(sectors(S)).row == first(sectors(S)).col || throw(ArgumentError("non-diagonal SumSpace $S"))
@@ -9,13 +9,13 @@ function Base.oneunit(S::SumSpace{Vect[IsingBimodule]})
 end
 
 function TensorKit.rightoneunit(S::SumSpace{Vect[IsingBimodule]})
-    @assert !isempty(S) "Cannot determine type of empty space"
+    @assert !isempty(sectors(S)) "Cannot determine type of empty space"
     allequal(a.col for a in sectors(S)) || throw(ArgumentError("sectors of $S do not have the same rightone"))
     return SumSpace(TensorKit.rightoneunit(first(S.spaces)))
 end
 
 function TensorKit.leftoneunit(S::SumSpace{Vect[IsingBimodule]})
-    @assert !isempty(S) "Cannot determine type of empty space"
+    @assert !isempty(sectors(S)) "Cannot determine type of empty space"
     allequal(a.row for a in sectors(S)) || throw(ArgumentError("sectors of $S do not have the same leftone"))
     return SumSpace(TensorKit.leftoneunit(first(S.spaces)))
 end

From 1f12902c38747837135aadab5afad236cc9811a5 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 26 Aug 2025 11:51:48 +0200
Subject: [PATCH 09/25] `left/rightoneunit` tests on empty `SumSpace`s

---
 test/vectorspaces/sumspace.jl | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index 3ceb7eb..1546d2e 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -144,6 +144,8 @@ end
     W = @constinferred SumSpace(U1Space(0 => 1))
     @test @constinferred(oneunit(V)) == W == @constinferred(oneunit(typeof(V)))
     @test @constinferred(leftoneunit(V)) == W == @constinferred(rightoneunit(V))
+    Vempty = @constinferred(SumSpace(zero(U1Space)))
+    @test oneunit(Vempty) == leftoneunit(Vempty) == rightoneunit(Vempty) == SumSpace(U1Space(0 => 1))
     @test @constinferred(⊕(V, V)) == SumSpace(vcat(V.spaces, V.spaces))
     @test @constinferred(⊕(V, oneunit(V))) == SumSpace(vcat(V.spaces, oneunit(V1)))
     @test @constinferred(⊕(V, V, V, V)) == SumSpace(repeat(V.spaces, 4))
@@ -217,6 +219,11 @@ end
     @test_throws ArgumentError("non-diagonal SumSpace $WM") oneunit(WM)
     @test_throws ArgumentError("non-diagonal SumSpace $WMop") oneunit(WMop)
 
+    Wempty = SumSpace(Vect[I]())
+    for f in (oneunit, leftoneunit, rightoneunit)
+        @test_throws ArgumentError("Cannot determine type of empty space") f(Wempty)
+    end
+
     VC = SumSpace(V1, V1)
     VCM = SumSpace(V1, V3)
     VMD = SumSpace(V2, V3)

From 1e928d33e604b7291fa9b6c48924d96afdc3a364 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Wed, 5 Nov 2025 14:34:14 +0100
Subject: [PATCH 10/25] delete specialisations to IsingBimodule

---
 src/vectorspaces/multifusionsumspace.jl | 60 -------------------------
 1 file changed, 60 deletions(-)
 delete mode 100644 src/vectorspaces/multifusionsumspace.jl

diff --git a/src/vectorspaces/multifusionsumspace.jl b/src/vectorspaces/multifusionsumspace.jl
deleted file mode 100644
index 0bd17e6..0000000
--- a/src/vectorspaces/multifusionsumspace.jl
+++ /dev/null
@@ -1,60 +0,0 @@
-# custom methods for SumSpaces
-
-function Base.oneunit(S::SumSpace{Vect[IsingBimodule]})
-    @assert !isempty(sectors(S)) "Cannot determine type of empty space"
-    allequal(a.row for a in sectors(S)) && allequal(a.col for a in sectors(S)) ||
-        throw(ArgumentError("sectors of $S are not all equal"))
-    first(sectors(S)).row == first(sectors(S)).col || throw(ArgumentError("non-diagonal SumSpace $S"))
-    return SumSpace(oneunit(first(S.spaces)))
-end
-
-function TensorKit.rightoneunit(S::SumSpace{Vect[IsingBimodule]})
-    @assert !isempty(sectors(S)) "Cannot determine type of empty space"
-    allequal(a.col for a in sectors(S)) || throw(ArgumentError("sectors of $S do not have the same rightone"))
-    return SumSpace(TensorKit.rightoneunit(first(S.spaces)))
-end
-
-function TensorKit.leftoneunit(S::SumSpace{Vect[IsingBimodule]})
-    @assert !isempty(sectors(S)) "Cannot determine type of empty space"
-    allequal(a.row for a in sectors(S)) || throw(ArgumentError("sectors of $S do not have the same leftone"))
-    return SumSpace(TensorKit.leftoneunit(first(S.spaces)))
-end
-
-function TensorKit.blocksectors(W::TensorMapSpace{SumSpace{Vect[IsingBimodule]},N₁,N₂}) where {N₁,N₂}
-    codom = codomain(W)
-    dom = domain(W)
-    if N₁ == 0 && N₂ == 0
-        return [IsingBimodule(1, 1, 0), IsingBimodule(2, 2, 0)]
-    elseif N₁ == 0
-        @assert N₂ != 0 "one of Type IsingBimodule doesn't exist"
-        return filter!(isone, collect(blocksectors(dom)))
-    elseif N₂ == 0
-        @assert N₁ != 0 "one of Type IsingBimodule doesn't exist"
-        return filter!(isone, collect(blocksectors(codom)))
-    elseif N₂ <= N₁ # keep intersection
-        return filter!(c -> TK.hasblock(codom, c), collect(blocksectors(dom)))
-    else
-        return filter!(c -> TK.hasblock(dom, c), collect(blocksectors(codom)))
-    end
-end
-
-function TensorKit.blocksectors(P::ProductSpace{SumSpace{Vect[IsingBimodule]},N}) where {N}
-    I = sectortype(P) # IsingBimodule
-    bs = Vector{I}()
-    if N == 0
-        return [IsingBimodule(1, 1, 0), IsingBimodule(2, 2, 0)]
-    elseif N == 1
-        for s in sectors(P)
-            push!(bs, first(s))
-        end
-    else
-        for s in sectors(P)
-            for c in ⊗(s...)
-                if !(c in bs)
-                    push!(bs, c)
-                end
-            end
-        end
-    end
-    return sort!(bs)
-end
\ No newline at end of file

From 92dfef0f39d0042eead42570e8ff4d23fadf9069 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Wed, 5 Nov 2025 14:39:37 +0100
Subject: [PATCH 11/25] remove include

---
 src/BlockTensorKit.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/BlockTensorKit.jl b/src/BlockTensorKit.jl
index 07ef4d8..e2bf9fb 100644
--- a/src/BlockTensorKit.jl
+++ b/src/BlockTensorKit.jl
@@ -40,7 +40,6 @@ import MatrixAlgebraKit as MAK
 # Spaces
 include("vectorspaces/sumspace.jl")
 include("vectorspaces/sumspaceindices.jl")
-include("vectorspaces/multifusionsumspace.jl")
 
 # Tensors
 include("tensors/abstractblocktensor/abstractblocktensor.jl")

From cc9e53db4274102c562f67eafd3d563e68e61241 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Wed, 5 Nov 2025 14:39:55 +0100
Subject: [PATCH 12/25] renaming from TK v0.15 + incoming renamings

---
 src/tensors/indexmanipulations.jl | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/src/tensors/indexmanipulations.jl b/src/tensors/indexmanipulations.jl
index 0b2d2df..85f1ce9 100644
--- a/src/tensors/indexmanipulations.jl
+++ b/src/tensors/indexmanipulations.jl
@@ -230,38 +230,38 @@ function TK.add_braid!(
     return TK.add_braid!(tdst, only(tsrc), (p₁, p₂), levels, α, β, backend...)
 end
 
-Base.@constprop :aggressive function TK.insertleftunit(
+Base.@constprop :aggressive function TK.insertleftunitspace(
         t::AbstractBlockTensorMap, i::Int = numind(t) + 1; kwargs...
     )
-    W = TK.insertleftunit(space(t), i; kwargs...)
+    W = TK.insertleftunitspace(space(t), i; kwargs...)
     tdst = similar(t, W)
     for (I, v) in nonzero_pairs(t)
         I′ = CartesianIndex(TT.insertafter(I.I, i - 1, (1,)))
-        tdst[I′] = TK.insertleftunit(v, i; kwargs...)
+        tdst[I′] = TK.insertleftunitspace(v, i; kwargs...)
     end
     return tdst
 end
 
-Base.@constprop :aggressive function TK.insertrightunit(
+Base.@constprop :aggressive function TK.insertrightunitspace(
         t::AbstractBlockTensorMap, i::Int = numind(t) + 1; kwargs...
     )
-    W = TK.insertrightunit(space(t), i; kwargs...)
+    W = TK.insertrightunitspace(space(t), i; kwargs...)
     tdst = similar(t, W)
     for (I, v) in nonzero_pairs(t)
         I′ = CartesianIndex(TT.insertafter(I.I, i, (1,)))
-        tdst[I′] = TK.insertrightunit(v, i; kwargs...)
+        tdst[I′] = TK.insertrightunitspace(v, i; kwargs...)
     end
     return tdst
 end
 
-Base.@constprop :aggressive function TK.removeunit(
+Base.@constprop :aggressive function TK.removeunitspace(
         t::AbstractBlockTensorMap, i::Int; kwargs...
     )
-    W = TK.removeunit(space(t), i)
+    W = TK.removeunitspace(space(t), i)
     tdst = similar(t, W)
     for (I, v) in nonzero_pairs(t)
         I′ = CartesianIndex(TT.deleteat(I.I, i))
-        tdst[I′] = TK.removeunit(v, i)
+        tdst[I′] = TK.removeunitspace(v, i)
     end
     return tdst
 end

From 05199695205e2dcd8e1db2fcb664c56dc12c5909 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Wed, 5 Nov 2025 14:40:10 +0100
Subject: [PATCH 13/25] more renamings

---
 src/vectorspaces/sumspace.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/vectorspaces/sumspace.jl b/src/vectorspaces/sumspace.jl
index 237ec78..2026dae 100644
--- a/src/vectorspaces/sumspace.jl
+++ b/src/vectorspaces/sumspace.jl
@@ -171,9 +171,9 @@ end
 TensorKit.unitspace(S::Type{<:SumSpace}) = SumSpace(TensorKit.unitspace(eltype(S)))
 TensorKit.zerospace(::Type{SumSpace{S}}) where {S} = SumSpace{S}()
 
-TensorKit.leftoneunit(S::SumSpace{<:GradedSpace}) = SumSpace(leftoneunit(first(S)))
+TensorKit.leftunitspace(S::SumSpace{<:GradedSpace}) = SumSpace(leftunitspace(first(S)))
 
-TensorKit.rightoneunit(S::SumSpace{<:GradedSpace}) = SumSpace(rightoneunit(first(S)))
+TensorKit.rightunitspace(S::SumSpace{<:GradedSpace}) = SumSpace(rightunitspace(first(S)))
 
 # Promotion and conversion
 # ------------------------

From 00c069b53b5e9fb2727542fab9c785fdf9a17bb7 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Wed, 5 Nov 2025 15:53:58 +0100
Subject: [PATCH 14/25] go back to `insertleft/rightunit` and `removeunit`

---
 src/tensors/indexmanipulations.jl | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/src/tensors/indexmanipulations.jl b/src/tensors/indexmanipulations.jl
index 85f1ce9..0b2d2df 100644
--- a/src/tensors/indexmanipulations.jl
+++ b/src/tensors/indexmanipulations.jl
@@ -230,38 +230,38 @@ function TK.add_braid!(
     return TK.add_braid!(tdst, only(tsrc), (p₁, p₂), levels, α, β, backend...)
 end
 
-Base.@constprop :aggressive function TK.insertleftunitspace(
+Base.@constprop :aggressive function TK.insertleftunit(
         t::AbstractBlockTensorMap, i::Int = numind(t) + 1; kwargs...
     )
-    W = TK.insertleftunitspace(space(t), i; kwargs...)
+    W = TK.insertleftunit(space(t), i; kwargs...)
     tdst = similar(t, W)
     for (I, v) in nonzero_pairs(t)
         I′ = CartesianIndex(TT.insertafter(I.I, i - 1, (1,)))
-        tdst[I′] = TK.insertleftunitspace(v, i; kwargs...)
+        tdst[I′] = TK.insertleftunit(v, i; kwargs...)
     end
     return tdst
 end
 
-Base.@constprop :aggressive function TK.insertrightunitspace(
+Base.@constprop :aggressive function TK.insertrightunit(
         t::AbstractBlockTensorMap, i::Int = numind(t) + 1; kwargs...
     )
-    W = TK.insertrightunitspace(space(t), i; kwargs...)
+    W = TK.insertrightunit(space(t), i; kwargs...)
     tdst = similar(t, W)
     for (I, v) in nonzero_pairs(t)
         I′ = CartesianIndex(TT.insertafter(I.I, i, (1,)))
-        tdst[I′] = TK.insertrightunitspace(v, i; kwargs...)
+        tdst[I′] = TK.insertrightunit(v, i; kwargs...)
     end
     return tdst
 end
 
-Base.@constprop :aggressive function TK.removeunitspace(
+Base.@constprop :aggressive function TK.removeunit(
         t::AbstractBlockTensorMap, i::Int; kwargs...
     )
-    W = TK.removeunitspace(space(t), i)
+    W = TK.removeunit(space(t), i)
     tdst = similar(t, W)
     for (I, v) in nonzero_pairs(t)
         I′ = CartesianIndex(TT.deleteat(I.I, i))
-        tdst[I′] = TK.removeunitspace(v, i)
+        tdst[I′] = TK.removeunit(v, i)
     end
     return tdst
 end

From e54130432f52397197d743550e11abf8da48d34f Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Wed, 5 Nov 2025 16:26:33 +0100
Subject: [PATCH 15/25] edit tests

---
 test/vectorspaces/sumspace.jl | 33 +++++++++++++++++----------------
 1 file changed, 17 insertions(+), 16 deletions(-)

diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index baa1505..6a8755a 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -185,7 +185,7 @@ end
     @test @constinferred(dual(V)) == @constinferred(conj(V)) == @constinferred(adjoint(V))
     @test field(V) == ℂ
 
-    @test_throws ArgumentError("sectors of $V are not all equal") oneunit(V)
+    @test unitspace(V) == unitspace(V1)
 
     @test @constinferred(sectortype(V)) == sectortype(V1)
     @test ((@constinferred sectors(V))...,) == (C1, C0, D1, D0, M) # ordering matters
@@ -198,23 +198,24 @@ end
     @test dim(@constinferred(typeof(V)())) == 0
     @test (sectors(typeof(V)())...,) == ()
 
-    # (left/right)oneunit tests
+    # (left/right)unitspace tests
     WC = @constinferred SumSpace(Vect[I](C0 => 1))
     WD = @constinferred SumSpace(Vect[I](D0 => 1))
     WM = @constinferred SumSpace(V3)
     WMop = @constinferred SumSpace(Vect[I](Mop => 1))
     for W in [WC, WD]
-        @test @constinferred(oneunit(W)) == W == @constinferred(leftoneunit(W)) == @constinferred(rightoneunit(W))
-        @test_throws ArgumentError("one of Type IsingBimodule doesn't exist") oneunit(typeof(W))
+        @test W == @constinferred(leftunitspace(W)) == @constinferred(rightunitspace(W))
+        @test unitspace(typeof(W)) == ⊞(Vect[IsingBimodule]((1, 1, 0) => 1, (2, 2, 0) => 1))
     end
 
-    @test leftoneunit(WMop) == WD && rightoneunit(WMop) == WC
-    @test leftoneunit(WM) == WC && rightoneunit(WM) == WD
-    @test_throws ArgumentError("non-diagonal SumSpace $WM") oneunit(WM)
-    @test_throws ArgumentError("non-diagonal SumSpace $WMop") oneunit(WMop)
+    @test leftunitspace(WMop) == WD && rightunitspace(WMop) == WC
+    @test leftunitspace(WM) == WC && rightunitspace(WM) == WD
+    @test unitspace(WM) == unitspace(WMop) == ⊞(Vect[IsingBimodule]((1, 1, 0) => 1, (2, 2, 0) => 1))
 
     Wempty = SumSpace(Vect[I]())
-    for f in (oneunit, leftoneunit, rightoneunit)
+    Wzero = zerospace(V)
+    @test unitspace(Wempty) == unitspace(Wzero)
+    for f in (leftunitspace, rightunitspace)
         @test_throws ArgumentError("Cannot determine type of empty space") f(Wempty)
     end
 
@@ -222,12 +223,12 @@ end
     VCM = SumSpace(V1, V3)
     VMD = SumSpace(V2, V3)
 
-    @test @constinferred(⊕(V, V)) == SumSpace(vcat(V.spaces, V.spaces))
-    @test @constinferred(⊕(VC, oneunit(VC))) == SumSpace(vcat(VC.spaces, oneunit(VC)))
-    @test @constinferred(⊕(VCM, leftoneunit(VCM))) == SumSpace(vcat(VCM.spaces, leftoneunit(VCM)))
-    @test @constinferred(⊕(VMD, rightoneunit(VMD))) == SumSpace(vcat(VMD.spaces, rightoneunit(VMD)))
+    @test @constinferred(⊞(V, V)) == SumSpace(vcat(V.spaces, V.spaces))
+    @test @constinferred(⊞(VC, unitspace(VC))) == SumSpace(vcat(VC.spaces, unitspace(VC)))
+    @test @constinferred(⊞(VCM, leftunitspace(VCM))) == SumSpace(vcat(VCM.spaces, leftunitspace(VCM)))
+    @test @constinferred(⊞(VMD, rightunitspace(VMD))) == SumSpace(vcat(VMD.spaces, rightunitspace(VMD)))
 
-    @test @constinferred(⊕(V, V, V, V)) == SumSpace(repeat(V.spaces, 4))
+    @test @constinferred(⊞(V, V, V, V)) == SumSpace(repeat(V.spaces, 4))
     @test @constinferred(fuse(VC, VC)) ≅ SumSpace(Vect[I](C0 => 8, C1 => 8))
     @test @constinferred(fuse(VC, VC', VC, VC')) ≅
         SumSpace(Vect[I](C0 => 128, C1 => 128))
@@ -239,9 +240,9 @@ end
     @test !(V ≻ ⊕(V, V))
 
     # blocksectors tests
-    @test @constinferred(blocksectors(one(V) ← one(V))) == [C0, D0]
+    @test @constinferred(blocksectors(one(V) ← one(V))) == (C0, D0)
     @test @constinferred(blocksectors(V ← V)) == sort(collect(sectors(V))) # convert set to vector
-    @test @constinferred(blocksectors(one(V))) == [C0, D0]
+    @test @constinferred(blocksectors(one(V))) == (C0, D0)
     for v in [VC, VCM, VMD]
         @test @constinferred(blocksectors(v^2)) == blocksectors(v ← v)
     end

From 5a7ea725fc1c7b275b7863bddf67e660b014b931 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Mon, 1 Dec 2025 17:40:56 +0100
Subject: [PATCH 16/25] add `isunitspace`

---
 src/vectorspaces/sumspace.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/vectorspaces/sumspace.jl b/src/vectorspaces/sumspace.jl
index 2026dae..4116aa5 100644
--- a/src/vectorspaces/sumspace.jl
+++ b/src/vectorspaces/sumspace.jl
@@ -172,8 +172,8 @@ TensorKit.unitspace(S::Type{<:SumSpace}) = SumSpace(TensorKit.unitspace(eltype(S
 TensorKit.zerospace(::Type{SumSpace{S}}) where {S} = SumSpace{S}()
 
 TensorKit.leftunitspace(S::SumSpace{<:GradedSpace}) = SumSpace(leftunitspace(first(S)))
-
 TensorKit.rightunitspace(S::SumSpace{<:GradedSpace}) = SumSpace(rightunitspace(first(S)))
+TensorKit.isunitspace(S::SumSpace{<:GradedSpace}) = all(isunitspace, S.spaces)
 
 # Promotion and conversion
 # ------------------------

From f97c6a7bff5b00fbc153caf413a80ee88ee6fede Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Mon, 1 Dec 2025 17:41:06 +0100
Subject: [PATCH 17/25] more tests

---
 test/vectorspaces/sumspace.jl | 13 ++++++++-----
 1 file changed, 8 insertions(+), 5 deletions(-)

diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index 6a8755a..2ac4743 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -204,10 +204,13 @@ end
     WM = @constinferred SumSpace(V3)
     WMop = @constinferred SumSpace(Vect[I](Mop => 1))
     for W in [WC, WD]
+        @test isunitspace(W)
         @test W == @constinferred(leftunitspace(W)) == @constinferred(rightunitspace(W))
         @test unitspace(typeof(W)) == ⊞(Vect[IsingBimodule]((1, 1, 0) => 1, (2, 2, 0) => 1))
     end
 
+    @test leftunitspace(V) == ⊞(WC, WD, WC)
+    @test rightunitspace(V) == ⊞(WC, WD, WD)
     @test leftunitspace(WMop) == WD && rightunitspace(WMop) == WC
     @test leftunitspace(WM) == WC && rightunitspace(WM) == WD
     @test unitspace(WM) == unitspace(WMop) == ⊞(Vect[IsingBimodule]((1, 1, 0) => 1, (2, 2, 0) => 1))
@@ -216,7 +219,7 @@ end
     Wzero = zerospace(V)
     @test unitspace(Wempty) == unitspace(Wzero)
     for f in (leftunitspace, rightunitspace)
-        @test_throws ArgumentError("Cannot determine type of empty space") f(Wempty)
+        @test_throws ArgumentError f(Wempty)
     end
 
     VC = SumSpace(V1, V1)
@@ -224,9 +227,9 @@ end
     VMD = SumSpace(V2, V3)
 
     @test @constinferred(⊞(V, V)) == SumSpace(vcat(V.spaces, V.spaces))
-    @test @constinferred(⊞(VC, unitspace(VC))) == SumSpace(vcat(VC.spaces, unitspace(VC)))
-    @test @constinferred(⊞(VCM, leftunitspace(VCM))) == SumSpace(vcat(VCM.spaces, leftunitspace(VCM)))
-    @test @constinferred(⊞(VMD, rightunitspace(VMD))) == SumSpace(vcat(VMD.spaces, rightunitspace(VMD)))
+    @test @constinferred(⊞(VCM, unitspace(VCM))) == SumSpace(vcat(VCM.spaces, unitspace(VCM).spaces))
+    @test @constinferred(⊞(VCM, leftunitspace(VCM))) == SumSpace(vcat(VCM.spaces, leftunitspace(VCM).spaces))
+    @test @constinferred(⊞(VMD, rightunitspace(VMD))) == SumSpace(vcat(VMD.spaces, rightunitspace(VMD).spaces))
 
     @test @constinferred(⊞(V, V, V, V)) == SumSpace(repeat(V.spaces, 4))
     @test @constinferred(fuse(VC, VC)) ≅ SumSpace(Vect[I](C0 => 8, C1 => 8))
@@ -242,7 +245,7 @@ end
     # blocksectors tests
     @test @constinferred(blocksectors(one(V) ← one(V))) == (C0, D0)
     @test @constinferred(blocksectors(V ← V)) == sort(collect(sectors(V))) # convert set to vector
-    @test @constinferred(blocksectors(one(V))) == (C0, D0)
+    @test @constinferred(blocksectors(one(V))) == [C0, D0]
     for v in [VC, VCM, VMD]
         @test @constinferred(blocksectors(v^2)) == blocksectors(v ← v)
     end

From e3ab406faec2b55817f1f55ac983e7b6cf436926 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Mon, 1 Dec 2025 17:43:21 +0100
Subject: [PATCH 18/25] format

---
 test/vectorspaces/sumspace.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index 2ac4743..a22a938 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -253,4 +253,4 @@ end
         @test isempty(@constinferred(blocksectors(v^2)))
         @test @constinferred(blocksectors(v ← v)) == blocksectors(v)
     end
-end
\ No newline at end of file
+end

From 4f07d8ba609446d0f5512d54c0013088a0523343 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Mon, 15 Dec 2025 11:29:43 +0100
Subject: [PATCH 19/25] check coloring of all component spaces + fix tests

---
 src/vectorspaces/sumspace.jl  | 23 +++++++++++++++++++++--
 test/vectorspaces/sumspace.jl |  6 ++++--
 2 files changed, 25 insertions(+), 4 deletions(-)

diff --git a/src/vectorspaces/sumspace.jl b/src/vectorspaces/sumspace.jl
index 4116aa5..810d398 100644
--- a/src/vectorspaces/sumspace.jl
+++ b/src/vectorspaces/sumspace.jl
@@ -171,8 +171,27 @@ end
 TensorKit.unitspace(S::Type{<:SumSpace}) = SumSpace(TensorKit.unitspace(eltype(S)))
 TensorKit.zerospace(::Type{SumSpace{S}}) where {S} = SumSpace{S}()
 
-TensorKit.leftunitspace(S::SumSpace{<:GradedSpace}) = SumSpace(leftunitspace(first(S)))
-TensorKit.rightunitspace(S::SumSpace{<:GradedSpace}) = SumSpace(rightunitspace(first(S)))
+function TensorKit.leftunitspace(S::SumSpace{<:GradedSpace})
+    I = sectortype(S)
+    if UnitStyle(I) isa GenericUnit
+        !isempty(sectors(S)) || throw(ArgumentError("Cannot determine the left unit of an empty SumSpace"))
+        TensorKit._allequal(leftunit, sectors(S)) ||
+            throw(ArgumentError("sectors of $S do not have the same left unit"))
+    end
+
+    return SumSpace(leftunitspace(first(S)))
+end
+
+function TensorKit.rightunitspace(S::SumSpace{<:GradedSpace})
+    I = sectortype(S)
+    if UnitStyle(I) isa GenericUnit
+        !isempty(sectors(S)) || throw(ArgumentError("Cannot determine the right unit of an empty SumSpace"))
+        TensorKit._allequal(rightunit, sectors(S)) ||
+            throw(ArgumentError("sectors of $S do not have the same right unit"))
+    end
+
+    return SumSpace(rightunitspace(first(S)))
+end
 TensorKit.isunitspace(S::SumSpace{<:GradedSpace}) = all(isunitspace, S.spaces)
 
 # Promotion and conversion
diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index a22a938..29f47d2 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -209,8 +209,10 @@ end
         @test unitspace(typeof(W)) == ⊞(Vect[IsingBimodule]((1, 1, 0) => 1, (2, 2, 0) => 1))
     end
 
-    @test leftunitspace(V) == ⊞(WC, WD, WC)
-    @test rightunitspace(V) == ⊞(WC, WD, WD)
+    @test_throws ArgumentError leftunitspace(V)
+    @test_throws ArgumentError rightunitspace(V)
+    @test leftunitspace(SumSpace(V1, V3)) == WC
+    @test rightunitspace(SumSpace(V2, V3)) == WD
     @test leftunitspace(WMop) == WD && rightunitspace(WMop) == WC
     @test leftunitspace(WM) == WC && rightunitspace(WM) == WD
     @test unitspace(WM) == unitspace(WMop) == ⊞(Vect[IsingBimodule]((1, 1, 0) => 1, (2, 2, 0) => 1))

From f7f1ac4e9d28c0442dd826f54ff7688d626cbe3d Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 16 Dec 2025 09:15:55 +0100
Subject: [PATCH 20/25] relax `isunitspace` dispatch but check zero spaces

---
 src/vectorspaces/sumspace.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/vectorspaces/sumspace.jl b/src/vectorspaces/sumspace.jl
index 810d398..fe6b1da 100644
--- a/src/vectorspaces/sumspace.jl
+++ b/src/vectorspaces/sumspace.jl
@@ -192,7 +192,7 @@ function TensorKit.rightunitspace(S::SumSpace{<:GradedSpace})
 
     return SumSpace(rightunitspace(first(S)))
 end
-TensorKit.isunitspace(S::SumSpace{<:GradedSpace}) = all(isunitspace, S.spaces)
+TensorKit.isunitspace(S::SumSpace) = !isempty(S) && all(isunitspace, S.spaces)
 
 # Promotion and conversion
 # ------------------------

From 1cf8e715beee084a15783ea36cac8fae92674d68 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 16 Dec 2025 09:18:12 +0100
Subject: [PATCH 21/25] use `oplus` instead of `sectors`

---
 src/vectorspaces/sumspace.jl | 19 ++-----------------
 1 file changed, 2 insertions(+), 17 deletions(-)

diff --git a/src/vectorspaces/sumspace.jl b/src/vectorspaces/sumspace.jl
index fe6b1da..9f658f6 100644
--- a/src/vectorspaces/sumspace.jl
+++ b/src/vectorspaces/sumspace.jl
@@ -172,25 +172,10 @@ TensorKit.unitspace(S::Type{<:SumSpace}) = SumSpace(TensorKit.unitspace(eltype(S
 TensorKit.zerospace(::Type{SumSpace{S}}) where {S} = SumSpace{S}()
 
 function TensorKit.leftunitspace(S::SumSpace{<:GradedSpace})
-    I = sectortype(S)
-    if UnitStyle(I) isa GenericUnit
-        !isempty(sectors(S)) || throw(ArgumentError("Cannot determine the left unit of an empty SumSpace"))
-        TensorKit._allequal(leftunit, sectors(S)) ||
-            throw(ArgumentError("sectors of $S do not have the same left unit"))
-    end
-
-    return SumSpace(leftunitspace(first(S)))
+    return SumSpace(leftunitspace(oplus(S)))
 end
-
 function TensorKit.rightunitspace(S::SumSpace{<:GradedSpace})
-    I = sectortype(S)
-    if UnitStyle(I) isa GenericUnit
-        !isempty(sectors(S)) || throw(ArgumentError("Cannot determine the right unit of an empty SumSpace"))
-        TensorKit._allequal(rightunit, sectors(S)) ||
-            throw(ArgumentError("sectors of $S do not have the same right unit"))
-    end
-
-    return SumSpace(rightunitspace(first(S)))
+    return SumSpace(rightunitspace(oplus(S)))
 end
 TensorKit.isunitspace(S::SumSpace) = !isempty(S) && all(isunitspace, S.spaces)
 

From 885b42db42000aa3d127e3852c2ff63f1e5a86ea Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 16 Dec 2025 09:20:04 +0100
Subject: [PATCH 22/25] relax more

---
 src/vectorspaces/sumspace.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/vectorspaces/sumspace.jl b/src/vectorspaces/sumspace.jl
index 9f658f6..b4d97a4 100644
--- a/src/vectorspaces/sumspace.jl
+++ b/src/vectorspaces/sumspace.jl
@@ -171,10 +171,10 @@ end
 TensorKit.unitspace(S::Type{<:SumSpace}) = SumSpace(TensorKit.unitspace(eltype(S)))
 TensorKit.zerospace(::Type{SumSpace{S}}) where {S} = SumSpace{S}()
 
-function TensorKit.leftunitspace(S::SumSpace{<:GradedSpace})
+function TensorKit.leftunitspace(S::SumSpace)
     return SumSpace(leftunitspace(oplus(S)))
 end
-function TensorKit.rightunitspace(S::SumSpace{<:GradedSpace})
+function TensorKit.rightunitspace(S::SumSpace)
     return SumSpace(rightunitspace(oplus(S)))
 end
 TensorKit.isunitspace(S::SumSpace) = !isempty(S) && all(isunitspace, S.spaces)

From 23d3fa42e13475c1b07415356f8e5b34a1595912 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 16 Dec 2025 09:22:48 +0100
Subject: [PATCH 23/25] use `issetequal`

---
 test/vectorspaces/sumspace.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index 29f47d2..1a609e4 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -246,7 +246,7 @@ end
 
     # blocksectors tests
     @test @constinferred(blocksectors(one(V) ← one(V))) == (C0, D0)
-    @test @constinferred(blocksectors(V ← V)) == sort(collect(sectors(V))) # convert set to vector
+    @test issetequal(@constinferred(blocksectors(V ← V)), sectors(V))
     @test @constinferred(blocksectors(one(V))) == [C0, D0]
     for v in [VC, VCM, VMD]
         @test @constinferred(blocksectors(v^2)) == blocksectors(v ← v)

From 3e5940fde621ad51b809ae033ba5bfd971e9b940 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 16 Dec 2025 09:24:28 +0100
Subject: [PATCH 24/25] another issetequal

---
 test/vectorspaces/sumspace.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/vectorspaces/sumspace.jl b/test/vectorspaces/sumspace.jl
index 1a609e4..7770ce1 100644
--- a/test/vectorspaces/sumspace.jl
+++ b/test/vectorspaces/sumspace.jl
@@ -245,7 +245,7 @@ end
     @test !(V ≻ ⊕(V, V))
 
     # blocksectors tests
-    @test @constinferred(blocksectors(one(V) ← one(V))) == (C0, D0)
+    @test issetequal(@constinferred(blocksectors(one(V) ← one(V))), (C0, D0))
     @test issetequal(@constinferred(blocksectors(V ← V)), sectors(V))
     @test @constinferred(blocksectors(one(V))) == [C0, D0]
     for v in [VC, VCM, VMD]

From 333a3224609b5253979a332d71c1a5007f6d8a38 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Tue, 23 Dec 2025 10:08:39 +0100
Subject: [PATCH 25/25] bump version

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 3ee008e..efa63b2 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "BlockTensorKit"
 uuid = "5f87ffc2-9cf1-4a46-8172-465d160bd8cd"
-version = "0.3.4"
+version = "0.3.5"
 authors = ["Lukas Devos <ldevos98@gmail.com> and contributors"]
 
 [deps]