On tau-tilting subcategories

Abstract The main theme of this paper is to study -tilting subcategories in an abelian category A with enough projective objects. We introduce the notion of -cotorsion torsion triples and investigate a bijection between the collection of -cotorsion torsion triples in A and the collection of support -tilting subcategories of A, generalizing the bijection by Bauer, Botnan, Oppermann, and Steen between the collection of cotorsion torsion triples and the collection of tilting subcategories of A. General definitions and results are exemplified using persistent modules. If A=Mod -R, where R is a unitary associative ring, we characterize all support -tilting (resp. all support ^- -tilting) subcategories of Mod -R in terms of finendo quasitilting (resp. quasicotilting) modules. As a result, it will be shown that every silting module (resp. every cosilting module) induces a support -tilting (resp. support ^- -tilting) subcategory of Mod -R. We also study the theory in Rep (Q, A), where Q is a finite and acyclic quiver. In particular, we give an algorithm to construct support -tilting subcategories in Rep (Q, A) from certain support -tilting subcategories of A.