Koszul-Morita duality

TL;DR

This paper generalizes Koszul duality to non-augmented algebras, linking it to Morita duality and broadening its applicability in algebraic contexts.

Contribution

It introduces a new form of Koszul duality that applies to non-augmented algebras, extending classical theories.

Findings

Established a generalized Koszul-Morita duality framework

Connected the new duality to classical Morita duality

Provided conditions under which the duality specializes to known cases

Abstract

We construct a generalization of Koszul duality in the sense of Keller--Lef\`evre for not necessarily augmented algebras. This duality is closely related to classical Morita duality and specializes to it in certain cases.