A Characterization of Finite EI Categories with Hereditary Category Algebras

Liping Li

Abstract.
In this paper we give an explicit algorithm to construct the ordinary 
quiver of a finite EI category for which the endomorphism groups
of all objects have orders invertible in the field k. We classify all finite
EI categories with hereditary category algebras, characterizing them 
as free EI categories (in a sense which we define) for which all
endomorphism groups of objects have invertible orders. Some applications
on the representation types of finite EI categories are derived.