  We introduce nominal string diagrams as, string diagrams internal in the
category of nominal sets. This requires us to take nominal sets as a monoidal
category, not with the cartesian product, but with the separated product. To
this end, we develop the beginnings of a theory of monoidal categories internal
in a symmetric monoidal category. As an instance, we obtain a notion of a
nominal PROP as a PROP internal in nominal sets. A 2-dimensional calculus of
simultaneous substitutions is an application.
