Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories
Algebraic Topology
2022-10-05 v4 Category Theory
K-Theory and Homology
Abstract
We show that the free construction from multicategories to permutative categories is a categorically-enriched non-symmetric multifunctor. Our main result then shows that the induced functor between categories of algebras is an equivalence of homotopy theories. We describe an application to ring categories.
Cite
@article{arxiv.2202.13659,
title = {Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories},
author = {Niles Johnson and Donald Yau},
journal= {arXiv preprint arXiv:2202.13659},
year = {2022}
}
Comments
45 pages. Final version as published in Theory and Applications of Categories. The main result here extends that of arXiv:2111.08653 to categories of algebras.