The MCM-approximation of the trivial module over a category algebra

Abstract

For a finite free EI category, we construct an explicit module over its category algebra. If in addition the category is projective over the ground field, the constructed module is a maximal Cohen–Macaulay approximation of the trivial module and is the tensor identity of the stable category of Gorenstein-projective modules over the category algebra. We give conditions on when the trivial module is Gorenstein-projective.