Relative homological categories (Q2381413)

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 \textit{F. Borceux} and \textit{D. Bourn} [``Mal'cev, protomodular, homological and semi-abelian categories'', Mathematics and its Applications 566, Kluwer (2004; Zbl 1061.18001) and \textit{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,\dots) are established.