A Characterization of Finite EI Categories with Hereditary Category Algebras

TL;DR

This paper provides an explicit algorithm to construct the quiver of certain finite EI categories, classifies those with hereditary algebras, and explores their representation types.

Contribution

It introduces a classification of finite EI categories with hereditary algebras as free EI categories with invertible endomorphism group orders.

Findings

Explicit algorithm for quiver construction

Classification of hereditary EI categories

Applications to representation types

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.