Definition 7.1 (Image, cover). We say a category $C$ has images if, for every $A\stackrel{f}{\to }B$ in $C$, there exists a least $m:B^{\prime }\rightarrowtail B$ in $\mathrm{Sub}(B)$ through which $f$ factors. We call $m$ the image of $f$, and we say $f$ is a cover if its image is $1_B$.

We write $A\stackrel{f}{⇾}B$ to indicate that $f$ is a cover.