Notation for the set of monomorphisms in $\mathrm{Hom}(A,B)$

Question

Let $\mathcal{C}$ be a small category, and let $A$ and $B$ be objects in $\mathcal{C}$. Is there any standard notation for the subset of all monomorphisms $A\hookrightarrow B$ in $\mathrm{Hom}(A,B)$? $\mathrm{Mon}(A,B)$ makes sense, but I've definitely never seen it before.

Answer 1

Given a category $C$, I have sometimes seen $C_m$ for the wide sub-category with monos only.

So you could indicate your monos only hom sets as:

$$Hom_{C_m}(A,B)$$

Using $Mon(A,B)$ is not a good idea, since it might be confused for a Hom set in the $Mon$ category of monoids