Extending (τ-)tilting subcategories and (co)silting modules

Abstract

Assume that B is a finite dimensional algebra, and (Formula presented.) is the one-point extension algebra of B using a finitely generated projective B-module P 0. The categories of B-modules and A-modules are connected via two adjoint functors known as the restriction and extension functors, denoted by (Formula presented.) and (Formula presented.), respectively. These functors have nice homological properties and have been studied in the category (Formula presented.) of finitely presented modules that we extend to the category (Formula presented.) of all A-modules. Our main focus is to investigate the behavior of important subcategories (tilting and τ-tilting subcategories) and objects (finendo quasi-tilting modules, silting modules, and cosilting modules) under these functors. © 2023 Taylor & Francis Group, LLC.