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

TL;DR

This paper introduces a novel approach to constructing model structures in extriangulated categories using left Frobenius pairs, establishing a correspondence with cotorsion pairs and generalizing existing results.

Contribution

It defines left Frobenius pairs in extriangulated categories and links them to cotorsion pairs, enabling new model structures to be constructed.

Findings

Established a bijective correspondence between Frobenius pairs and cotorsion pairs.

Constructed new admissible model structures from left Frobenius pairs.

Generalized previous results on model structures in extriangulated categories.

Abstract

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 C, and then establish a bijective correspondence between Frobenius pairs and certain cotorsion pairs in 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).