English

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.

Keywords

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.

R2 v1 2026-06-24T09:56:01.517Z