  The functor that takes a ring to its category of modules has an adjoint if
one remembers the forgetful functor to abelian groups: the endomorphism ring of
linear natural transformations. This uses the self-enrichment of the category
of abelian groups. If one considers enrichments into symmetric sequences or
even bisymmetric sequences, one can produce an endomorphism operad or an
endomorphism prop.
  In this note, we show that more generally, given an category C enriched in a
monoidal category V, the functor that associates to a monoid in V its category
of representations in C is adjoint to the functor that computes the
endomorphism monoid of any functor with domain C. After describing the first
results of the theory we give several examples of applications.
