Let $\mathcal{C}$ be a category. Consider the following statement:
(S1) Whenever $A,B$ are objects and $\iota_1:A\to B$ and $\iota_2:B\to A$ are monomorphisms, then there is an isomorphism $\phi:A\to B$.
(For instance, (S1) holds in the category of groups, but not in the category of topological spaces with continuous maps.)
Let (S2) be the statement that we get from (S1) by replacing "mono" by "epi". Are (S1) and (S2) equivalent?