A bijection between support $\tau$-tilting subcategories and $\tau$-cotorsion pairs in extriangulated categories

Abstract

Let $\mathscr{C}$ be an extriangulated category with enough projectives and injectives. We give a new definition of tilting subcategories of $\mathscr{C}$ and prove it coincides with the definition given in [19]. As applications, we introduce the notions of support $\tau$-tilting subcategories and $\tau$-cotorsion pairs of $\mathscr{C}$. We build a bijection between support $\tau$-tilting subcategories and certain $\tau$-cotorsion pairs. Moreover, this bijection induces a bijection between tilting subcategories and certain cotorsion pairs.