Koszul duality in exact categories

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.