Enriched Koszul duality

Eurenius, B. (2024) Enriched Koszul duality. Journal of Homotopy and Related Structures, 19 (3). pp. 397-429. ISSN 2193-8407

Abstract

We show that the category of non-counital conilpotent dg-coalgebras and the category of non-unital dg-algebras carry model structures compatible with their closed non-unital monoidal and closed non-unital module category structures respectively. Furthermore, we show that the Quillen equivalence between these two categories extends to a non-unital module category Quillen equivalence, i.e. providing an enriched form of Koszul duality.