## § monic and epic arrows

This is trivial, I'm surprised it took me *this long * to internalize this fact.
When we convert a poset $(X, \leq)$ into a category, we stipulate that
$x \rightarrow y \iff x \leq y$.
If we now consider the category $Set$ of sets and functions between sets,
and arrow $A \xrightarrow{f} B$ is a function from $A$ to $B$. If $f$ is
monic, then we know that $|A| = |Im(f)| \leq |B|$. That is, a monic arrow
behaves a lot like a poset arrow!
Similarly, an epic arrow behaves a lot like the arrow in the inverse poset.
I wonder if quite a lot of category theoretic diagrams are clarified by thinking
of monic and epic directly in terms of controlling sizes.