Koszul duality in exact categories

TL;DR

This paper extends Koszul duality theory to chain complexes in exact categories, generalizing existing results and providing new applications, notably in the context of bornological spaces over Banach fields.

Contribution

It introduces Koszul duality results in exact categories, generalizing Vallette's and Lurie's theorems, and applies these to categories of bornological spaces.

Findings

Generalized Vallette's cooperadic Koszul duality theorem

Extended operadic Koszul duality to exact categories

Applied duality results to bornological spaces over Banach fields

Abstract

In this paper we establish Koszul duality type results in the setting of chain complexes in exact categories. In particular we prove generalisations of Vallette's cooperadic Koszul duality theorem, and operadic Koszul duality along the lines of Lurie. We also prove a connective version. We conclude with some applications, including our main example, the category of complete bornological spaces over a Banach field.