ON TAU-TILTING SUBCATEGORIES

ASADOLLAHI, JAVAD; SADEGHI, SOMAYEH; TREFFINGER, HIPOLITO

CANADIAN JOURNAL OF MATHEMATICS

CANADIAN MATHEMATICAL SOC

Año: 2024 p. 1 - 34

0008-414X

The main theme of this paper is to study τ-tilting subcategories in an abelian category A with enough projective objects. We introduce the notion of τ-cotorsion torsion triples and investigate a bijection between the collection of τ-cotorsion torsion triples in A and the collection of support τ -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 τ-tilting, resp. all support τ−-tilting, subcategories of Mod-R in term of finendo quasitilting, resp. quasicotilting, modules. As a result, it will be shown that every silting module, respectively every cosilting module, induces a support τ-tilting, respectively support τ−-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 τ-tilting subcategories in Rep(Q, A ) from certain support τ -tilting subcategories of A .