# Semantics

Premonoidal structure (together with an interpretation of base types and constructors) is exactly what is required to give a semantics of process terms. For example:

- V C StateZ(C), where StateZ(C)[X,Y] is C[X Z,Y Z].

- V VT VU, where T is any commutative monad satisfying the monic condition, U is any monad satisfying the monic condition, and there is an appropriate natural transform from T to U.

- Term() Term(,) Term(,,).

- Graph() Graph(,) Graph(,,).

Proposition Graph(,,) is the initial strict symmetric premonoidal category over over with Graph(,) as its centre.