nLab
symmetric multicategory

Contents

Context

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

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.

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.

References

Fuentes-Keuthan2019?

Daniel Fuentes-Keuthan?, Modeling connective spectra via multicategories, arXiv:1909.11148

Last revised on March 1, 2021 at 14:58:46. See the history of this page for a list of all contributions to it.