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If objects $A$ and $B$ (in some category $\mathcal{C}$) are isomorphic, and if some morphism $\gamma:A \rightarrow B$ is monic, does it follow that $\gamma$ is also epic?


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up vote 6 down vote accepted

This isn't even true in Set. For example, $f:\mathbb{N} \rightarrow \mathbb{N}$, $f(n)=n+1$ is monic but not epic.

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