  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, $\mathbf{Perm}$, which is not a
symmetric monoidal closed model category. The right adjoint of this Quillen
equivalence is the classical Segal's Nerve functor.
