  This paper is about skew monoidal tensored V-categories (= skew monoidal
hommed V-actegories) and their categories of modules. A module over <M,*,R> is
an algebra for the monad T = R * _ on M. We study in detail the skew monoidal
structure of M^T and construct a skew monoidal forgetful functor from M^T to
the category of E-objects in M where E=M(R,R) is the endomorphism monoid of the
unit object R. Then we give conditions for the forgetful functor to be strong
monoidal and for the category M^T of modules to be monoidal. In formulating
these conditions a notion of `self-cocomplete' subcategories of presheaves
appears to be useful which provides also some insight into the problem of
monoidality of the skew monoidal structures found by Altenkirch, Chapman and
Uustalu on functor categories [C,M].
