Janelidze, Tamar Relative homological categories. (English) Zbl 1127.18007 J. Homotopy Relat. Struct. 1, No. 1, 185-194 (2006). 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. Reviewer: Antonio R. Garzón (Granada) Cited in 1 ReviewCited in 7 Documents 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 Keywords:relative homological category; normal epimorphism; protomodular category Citations:Zbl 1061.18001; Zbl 0756.18007 PDFBibTeX XMLCite \textit{T. Janelidze}, J. Homotopy Relat. Struct. 1, No. 1, 185--194 (2006; Zbl 1127.18007) Full Text: arXiv EuDML EMIS