short exact sequence

English

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

Noun

short exact sequence (plural short exact sequences)

1. (homological algebra) An exact sequence of the form $0\to A\to B\to C\to 0$.