# nLab symmetric multicategory

### Context

#### Monoidal categories

monoidal categories

category theory

# Contents

## Idea

A symmetric multicategory is a multicategory equipped with an action of the symmetric group $S_n$ on the set of $n$-ary operations, for all $n$, 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)