Journal of Soviet Mathematics

, Volume 19, Issue 1, pp 1060-1067

First online:

Homological algebra in pre-Abelian categories

  • A. V. Yakovlev

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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.