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 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 En-ring categories for 1 ≤ n ≤ ∞.