  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.
