Relative torsion classes, relative tilting, and relative silting modules

Abstract

Let Λ be an Artin algebra. In 2014, Adachi, Iyama, and Reiten proved that the torsion functorially finite classes in can be described by the τ-tilting theory. The aim of this paper is to introduce the notion of F-torsion class in where F is an additive subfunctor of and to characterize when these classes are preenveloping and F-preenveloping. In order to do that, we introduce the notion of F-presilting Λ-module. The latter is both a generalization of τ-rigid and F-tilting in