nLab
symmetric multicategory

Context

Monoidal categories

Category theory

Contents

Idea

A symmetric multicategory is a multicategory equipped with an action of the symmetric group S nS_n on the set of nn-ary operations, for all nn, such that composition respects this action.

Symmetric multicategories are equivalently called coloured symmetric operads over Set. See there for more details.

Properties

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 (89.204.139.207)