This paper is about skew monoidal tensored fbac26c027bbcbe1e654f0607" title="Click to view the MathML source">V-categories (= skew monoidal hommed fbac26c027bbcbe1e654f0607" title="Click to view the MathML source">V-actegories) and their categories of modules. A module over 〈M,⁎,R〉 is an algebra for the monad on M. We study in detail the skew monoidal structure of MT and construct a skew monoidal forgetful functor 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 MT 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].