×

Relative homological categories. (English) Zbl 1127.18007

The author uses a distinguished class of normal epimorphisms, in a pointed category \({\mathcal C}\) with finite limits and cokernels, to introduce notions of relative homological and weakly homological categories. In this way, a generalization of homological and protomodular categories, in the sense of F. Borceux and D. Bourn [“Mal’cev, protomodular, homological and semi-abelian categories”, Mathematics and its Applications 566, Kluwer (2004; Zbl 1061.18001) and D. Bourn, Lect. Notes Math. 1448, 43–62 (1991; Zbl 0756.18007)], is obtained and then, relative versions of standard homological lemmas (snake lemma, \(3\times 3\)-lemma,…) are established.

MSC:

18G25 Relative homological algebra, projective classes (category-theoretic aspects)
18G50 Nonabelian homological algebra (category-theoretic aspects)
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
PDFBibTeX XMLCite
Full Text: arXiv EuDML EMIS