, Volume 19, Issue 1, pp 1060-1067

Homological algebra in pre-Abelian categories

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We construct derived functors in additive categories in which each morphism has a kernel, co-kernel, image, and coimage, but the image and coimage are not necessarily isomorphic. We prove that these derived functors possess the usual properties. The main difficulty is that the 3×3-lemma does not necessarily hold in the categories under consideration.

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 94, pp. 131–141, 1979.