diff --git a/src/spaces/homspace.jl b/src/spaces/homspace.jl
index 9ef8a5d51..f1819572e 100644
--- a/src/spaces/homspace.jl
+++ b/src/spaces/homspace.jl
@@ -56,10 +56,15 @@ const TensorMapSpace{S <: ElementarySpace, N₁, N₂} = HomSpace{
 numout(::Type{TensorMapSpace{S, N₁, N₂}}) where {S, N₁, N₂} = N₁
 numin(::Type{TensorMapSpace{S, N₁, N₂}}) where {S, N₁, N₂} = N₂
 
+Base.length(W::HomSpace) = numout(W) + numin(W)
 function Base.getindex(W::TensorMapSpace{<:IndexSpace, N₁, N₂}, i) where {N₁, N₂}
     return i <= N₁ ? codomain(W)[i] : dual(domain(W)[i - N₁])
 end
 
+Base.Broadcast.broadcastable(W::HomSpace) =
+    TupleTools.vcat(identity.(codomain(W)), dual.(domain(W)))
+Base.map(f, W::HomSpace) = f.(W)
+
 function ←(codom::ProductSpace{S}, dom::ProductSpace{S}) where {S <: ElementarySpace}
     return HomSpace(codom, dom)
 end
diff --git a/test/symmetries/spaces.jl b/test/symmetries/spaces.jl
index 0438a7e14..6296bc335 100644
--- a/test/symmetries/spaces.jl
+++ b/test/symmetries/spaces.jl
@@ -444,6 +444,8 @@ end
         @test W[3] == V5
         @test W[4] == V4
         @test W[5] == V3
+        @test all(W .== (V1, V2, V5, V4, V3))
+        @test @constinferred(map(isdual, W)) == ntuple(i -> isdual(W[i]), length(W))
         @test @constinferred(hash(W)) == hash(deepcopy(W)) != hash(W')
         @test W == deepcopy(W)
         cod = codomain(W)