Multicategories from Symmetric Monoidal Categories
Category Theory
2025-08-04 v3
Abstract
This paper considers the possible underlying multicategories for a symmetric monoidal category, and shows that, up to canonical and coherent isomorphism, there really is only one. As a result, there is a well-defined forgetful functor from symmetric monoidal categories to multicategories, as long as all morphisms of symmetric monoidal categories are at least lax symmetric monoidal. The paper also shows that this forgetful functor has a weak left adjoint, and that the monad of the adjunction gives a strictification construction.
Cite
@article{arxiv.2308.00656,
title = {Multicategories from Symmetric Monoidal Categories},
author = {A. D. Elmendorf},
journal= {arXiv preprint arXiv:2308.00656},
year = {2025}
}
Comments
Revised following referee's report, and slightly reorganized from previous version