  Categories are coreflectively embedded in multicategories via the "discrete
cocone" construction, the right adjoint being given by the monoid construction.
Furthermore, the adjunction lifts to the "cartesian level": preadditive
categories are coreflectively embedded (as theories for many-sorted modules) in
cartesian multicategories (general algebraic theories). In particular, one gets
a direct link between two ways of considering modules over a rig, namely as
additive functors valued in commutative monoids or as models of the theory
generated by the rig itself.
