# nLab homological category

References

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-Hölder theorem.

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

## References

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