  The analogy between Yetter's deformation theory form (lax) monoidal functors
and Gerstenahaber's deformation theory for associative algebras is solidified
by shown that under reasonable conditions the category of functors with an
action of a lax monoidal functor is abelian, that an analogue of the Hochschild
cohomology of an algebra with coefficients in a bimodule exists for monoidal
functors, and is given by right derived functors. The deformation cohmology of
a monoidal natural transformation is shown to be a special case.
