Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories

Niles Johnson and Donald Yau

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: multicategory, permutative category, homotopy equivalence, operad algebra

2020 MSC: Primary: 18M65; Secondary: 55P42, 18M05

Theory and Applications of Categories, Vol. 38, 2022, No. 30, pp 1156-1208.

Published 2022-10-04.


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