homological category

A category $C$ 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 the Jordan-HÃ¶lder theorem.

A homological category which is Barr-exact and has finite coproducts is semiabelian.

- Dominique Bourn, Francis Borceux, Mal'cev, protomodular, homological and semi-abelian categories, Kluwer 2004.

Revised on October 16, 2014 12:10:09
by David Corfield
(87.114.92.4)