Tilting Torsion-Free Classes in the Category of Comodules

Abstract

A well-known Assem–Smal $$\phi $$ theorem on tilting modules plays an important role in tilting theory. In this paper, we prove that a version of Assem–Smal $$\phi $$ theorem still holds in the category of comodules. Following this result, we characterize the tilting torsion-free classes in the category of comodules using the precover theory.