Homotopy theory in additive categories with suspensions

Abstract

We develop a homotopy theory in additive categories endowed with additive endofunctors, analogous to Quillen’s model categories theory. As applications, we show that Iyama–Yoshino triangulated subfactor categories can be modeled; we prove that Verdier quotients can be realized as triangulated subfactors in some cases; we construct the homotopy theory of Hovey triples in arbitrary exact categories.