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.