Hereditary cotorsion pairs on extriangulated subcategories

Abstract

Let $\mathcal{B}$ be an extriangulated category with enough projectives and enough injectives. We define a proper $m$-term subcategory $\mathcal{G}$ on $\mathcal{B}$, which is an extriangulated subcategory. Then we give a correspondence between cotorsion pairs on $\mathcal{G}$, support $\tau$-tilting subcategories on an abelian quotient of $\mathcal{G}$ when $m=2$. If such $\mathcal{G}$ is induced by a hereditary cotorsion pair, then we give a correspondence between cotorsion pairs on $\mathcal{G}$ and intermediate cotorsion pairs on $\mathcal{B}$ under certain assumptions. At last, we study an important property of such extriangulated subcategory $\mathcal{G}$.

18 pages

Cited by in corpus (1)

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