A morphism $f \colon x \to y$ in a category is
- a monomorphism if for any parallel morphisms $h,k \colon w \rightrightarrows x$, $fh = fk$ implies that $h=k$; or
- an epimorphism if for any parallel morphisms $h,k \colon y \rightrightarrows z$, $hf=kf$ implies that $h=k$.