nLab
homological category

A category CC is homological if it is pointed, regular and protomodular.

Many of the standard results of classical homological algebra in abelian categories extend to homological categories: the five lemma, the nine lemma, the snake lemma, long exact sequence in homology, the Noether isomorphism theorem. There is also a version of Jordan-Hoelder theorem.

Revised on May 3, 2014 22:41:46 by Fosco Loregian (91.255.7.162)