  This semi-expository work covers central aspects of the theory of relative
tensor products as developed in Higher Algebra, as well as their application to
Koszul duality for algebras in monoidal oo-categories. Part of our goal is to
expand on the rather condensed account of loc. cit. Along the way, we
generalize various aspects of the theory. For instance, given a monoidal
oo-category Cc, an oo-category Mm which is left-tensored over Cc, and an
algebra A in Cc, we construct an action of A-A-bimodules N in Cc on left
A-modules M in Mm by an "external relative tensor product" N \otimes_A M. (Up
until now, even the special ("internal") case Cc = Mm appears to have escaped
the literature.
  As an application, we generalize the Koszul duality of loc. cit. to include
modules. Our straightforward approach requires that we at this point assume
certain compatibilities between tensor products and limits; these assumptions
have recently been shown to be unnecessary in work by Brantner, Campos and
Nuiten (arXiv:2104.03870).
