A new method to construct model structures from left Frobenius pairs in extriangulated categories

Abstract

<abstract><p>Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. In this paper, we first introduce the concept of left Frobenius pairs on an extriangulated category $ \mathcal{C} $, and then establish a bijective correspondence between left Frobenius pairs and certain cotorsion pairs in $ \mathcal{C} $. As an application, some new admissible model structures are established from left Frobenius pairs under certain conditions, which generalizes a result of Hu et al. (J. Algebra 551 (2020) 23–60).</p></abstract>