A generalized Koszul theory and its application

TL;DR

This paper extends classical Koszul theory to graded algebras with self-injective degree-zero parts, broadening its applicability to directed and EI categories.

Contribution

It introduces a generalized Koszul theory assuming $A_0$ is self-injective, expanding classical results to new algebraic contexts.

Findings

Generalized Koszul theory for self-injective $A_0$

Application to directed categories and finite EI categories

Broader framework for Koszul duality

Abstract

Let $A$ be a graded algebra. In this paper we develop a generalized Koszul theory by assuming that $A_0$ is self-injective instead of semisimple and generalize many classical results. The application of this generalized theory to directed categories and finite EI categories is described.