Monos and epis in MSet

[0xd34df00d]

aluffi/ch1/solutions.tex

Line 1159 in 7d18db3

\item A multiset-function $f:\hat{S}\to\hat{T}$ is a monomorphism iff for all

I'm not sure that's the case. Consider $A = { a, b, c }$ with $~_A$ being the reflexive transitive symmetric closure of $a ~_A b$, and $B = { 1, 2, 3 }$ with any pair of elements belonging to $~_B$. Arbitrary injection from A to B would then be a monomorphism, but it does not preserve the relation backwards.

[srcreigh]

Thank you very much for reading the solutions. Unfortunately I can no longer tell left from right with regards to these problems. I will leave this open in case I get back to it, or in case you or someone else would like to shed more light on the issue. Perhaps you would like to share your solution to this problem?

[0xd34df00d]

Haha, I won't be able to tell left from right too in a couple of years!

For my definition of the multisets (which I believe coincides with yours) the only thing that holds is the same as for the usual sets: injectivity and surjectivity. See also my question on StackExchange: https://math.stackexchange.com/questions/3165195/describing-the-monomorphisms-and-epimorphisms-in-the-category-of-multisets