short exact sequence

Diagram of a short exact sequence ${\displaystyle 0{\xrightarrow {z}}A{\xrightarrow {i}}B{\xrightarrow {s}}C{\xrightarrow {c}}0}$; actually the diagram suggests a model thereof in category ${\displaystyle \mathbf {Set} }$ (or any category that has a forgetful functor to ${\displaystyle \mathbf {Set} }$). Function i is an injection and function s a surjection. Function c is constant. The image ${\displaystyle i(A)}$ equals A’, and C is isomorphic to the quotient B modulo A’.