# nLab symmetric multicategory

Contents

### 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.

### Thomason model structure

A full subcategory of based symmetric multicategories admit a Thomason-style model structure that is Quillen equivalent to connective spectra, according to [Fuentas-Keuthan].

\bibitem{Fuentas-Keuthan} Modeling connective spectra via multicategories, Daniel Fuentes-Keuthan?

Last revised on September 26, 2019 at 18:18:23. See the history of this page for a list of all contributions to it.