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 the Jordan-Hölder theorem.

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

References

Revised on November 3, 2016 05:48:33 by David Corfield (51.6.72.106)