With duals for objects
With duals for morphisms
Special sorts of products
In higher category theory
A symmetric multicategory is a multicategory equipped with an action of the symmetric group on the set of -ary operations, for all , such that composition respects this action.
Symmetric multicategories are equivalently called coloured symmetric operads over Set. See there for more details.
Closed monoidal structure
With respect to the Boardman-Vogt tensor product (see there for details) symmetric multicategories form a closed symmetric monoidal category.
Revised on February 23, 2012 12:32:36
by Urs Schreiber