short exact sequence

English

Diagram of a short exact sequence $0\stackrel{z}{\to }A\stackrel{i}{\to }B\stackrel{s}{\to }C\stackrel{c}{\to }0$; actually the diagram suggests a model thereof in category $𝐒𝐞𝐭$ (or any category that has a forgetful functor to $𝐒𝐞𝐭$). 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 $0\to A\to B\to C\to 0$.