In this paper we construct a symmetric monoidal closed model category of coherently commutative monoidal categories. The main aim of this paper is to establish a Quillen equivalence between a model category of coherently commutative monoidal categories and a natural model category of Permutative (or strict symmetric monoidal) categories, Perm, which is not a symmetric monoidal closed model category. The right adjoint of this Quillen equivalence is the classical Segal's Nerve functor.
Keywords: Segal's Nerve functor, Theory of Bicycles, Leinster construction
2020 MSC: 18M05, 18M60, 18N55, 18F25, 55P42, 19D23
Theory and Applications of Categories, Vol. 35, 2020, No. 14, pp 417-512.