<abstract><p>Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact triangulated categories. In this paper, we first introduce the concept left Frobenius pairs on an extriangulated category $ \mathcal{C} $, then establish bijective correspondence between certain cotorsion in $. As application, some new admissible model structures are ...

In this article, we show that the localization of an extriangulated category by a multiplicative system satisfying mild assumptions can be equipped with natural, universal structure category. This construction unifies Serre quotient abelian categories and Verdier triangulated categories. Indeed give such for bit wider class morphisms, so it covers several other localizations appeared in literat...