Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories

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.

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.