  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.
