Let $R\to A$ be a homomorphism of associative rings, and let $(\mathcal F,\mathcal C)$ hereditary complete cotorsion pair in $R\mathsf{-Mod}$. F_A,\mathcal C_A)$ the $A\mathsf{-Mod}$ which $\mathcal F_A$ is class all left $A$-modules whose underlying $R$-modules belong to F$. Assuming that F$-resolution dimension every $R$-module finite F$ preserved by coinduction functor $\operatorname{Hom}_R(...

<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 ...