2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115634We introduce relative homological and weakly homological categories, where ``relative'' refers to a distinguished class of normal epimorphisms. 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 relative homological category.to be published in "Journal of Homotopy and Related Structures"Category Theorytext