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Relative homological categories
#
Relative homological categories

##
Tamar Janelidze

We introduce relative homological and weakly homological
categories $(\mathbf{C},\mathbf{E})$, where ``relative'' refers to a
distinguished class $\mathbf{E}$ of normal epimorphisms in
$\mathbf{C}$. 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 relative homological category.

Journal of Homotopy and Related Structures, Vol. 1(2006), No. 1, pp. 185-194
http://jhrs.rmi.acnet.ge/volumes/2006/n1a8/