An inverse category can be defined as a category where every $f$ admits a unique regular inverse, i.e. a map $g$ such that $fgf=f$ and $gfg=g$. In [1], Kastl proves that any locally small inverse category admits a faithful functor into $PInj$, the category of sets and partial injections. The proof first verifies Isbell's criterion, obtaining a faithful functor to $Set$ and then one proves a general result giving rise to a faithful functor to $PInj$.


[1] J. Kastl. Inverse categories. Studien zur Algebra und ihre Anwendungen, 7:51–
60, 1979.