On faithfully balanced modules, F-cotilting and F-Auslander algebras

The aim of this paper is to give a unification of the theory of (co)tilting modules and (higher) Auslander correspondence by using faithfully balanced modules (i.e., faithful modules with the double centralizer property). In the language of relative homological algebra following Auslander-Solberg, a relative version of faithfully balancedness is given, which will be called 1-F-faithful. The relative versions of (higher) Auslander correspondence and Brenner-Butler theorem are also developed. (C) 2020 Elsevier Inc. All rights reserved.