Stable categories and triangulated equivalences

Abstract

Extriangulated categories are a generalization of triangular categories and exact categories, and many important conclusions can be unified under this framework. In this paper, the localized quotient induced by the model structure is realized by the ideal quotient in the extriangulated category, i.e., the triangulated equivalence between the two quotient categories is established. At the same time, this result is also applied to the Frobenius exact category, the homotopy category of a ring $R$, and the stable category of Gorenstein objects.