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We introduce relative homological and weakly homological categories (C, E), where " relative " refers to a distinguished class E of normal epimorphisms in C. It is a generalization of homological categories, but also protomodular categories can be regarded as examples. We indicate that the relative versions of various homological lemmas can be proved in a… (More)

- Tamar Janelidze
- Applied Categorical Structures
- 2009

- TAMAR JANELIDZE
- 2011

The direction of abelian relative homological algebra based on relative exactness properties was initiated by N. Yoneda, whose quasi-abelian categories [4] can be seen as additive categories equipped with a distinguished class E of epimorphisms, so that the short exact sequences K → A → B with A → B in E have the same properties as all short exact sequences… (More)

The purpose of this paper is to prove a new, incomplete-relative, version of Non-abelian Snake Lemma, where " relative " refers to a distinguished class of normal epimorphisms in the ground category, and " incomplete " refers to omitting all complete-ness/cocompleteness assumptions not involving that class.

- Tamar Janelidze
- Applied Categorical Structures
- 2011

- Zurab Janelidze, Gareth Boxall, +7 authors Ingrid Rewitzky
- 2010

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