On the representation types of category algebras of finite EI categories

A finite EI category is a small category with finitely many morphisms such that every endomorphism is an isomorphism. They include finite groups, finite posets and free categories of finite quivers as special cases. In this paper we consider category algebras of finite EI categories with two or three objects, describe some criteria for finite representation type, and classify the representation types for certain classes of finite EI categories with extra properties.