Homological algebra in pre-Abelian categories
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.
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- 1.I. Bucur and A. Deleanu, Introduction to the Theory of Categories and Functors, Wiley, London-New York-Sydney (1968).Google Scholar