Natural multitransformations of multifunctors

We continue to develop the theory of multicategories over verbal categories. This theory includes both the usual category theory and the theory of operads, as well as a significant part of the classical universal algebra. We introduce the notion of natural multitransformations of multifunctors, owing to which categories of multifunctors from a multicategory to another one turn into multicategories. In particular, any algebraic variety over a multicategory possesses a natural structure of a multicategory. Furthermore, we construct a multicategory analog of comma-categories with properties similar to the category case. We define the notion of the center of a multicategory and show that centers of multicategories are commutative operads (introduced by us earlier) and only they. We prove that the notion of a commutative FSet-operad coincides with the notion of a commutative algebraic theory.