We’re brought up to say that the dual concept of injection is surjection, and of course there’s a perfectly good reason for this. The monics in the category of sets are the injections, the epics are ...

Example Let A be the category (0 → 1) consisting of a single nontrivial map. Then an object of SetobA is a pair (P0, P1) of sets, and an object of SetA is a function X0 f → X1 between a pair of ...