Epimorphism

Collection

context	${\bf C}$ … category
definiendum	$f \in\mathrm{it}$
inclusion	$f:{\bf C}[A,B]$
postulate	$\langle B,\prod_{B}1_A\rangle$ … pushout of $f$ along itself

Discussion

See Monomorphism.

In ${\bf{Set}}$ the epimorphisms are the surjections. But people like to point out that in general, epis are quite different from surjections and also more difficult to classify (as opposed to monos, which mostly behave exactly like injections). See the nLab link below for variations (or rather further restrictions) of the concept.