  In this paper we construct a symmetric monoidal closed model category of
coherently commutative Picard groupoids. We construct another model category
structure on the category of (small) permutative categories whose fibrant
objects are (permutative) Picard groupoids. The main result is that the Segal's
nerve functor induces a Quillen equivalence between the two aforementioned
model categories. Our main result implies the classical result that Picard
groupoids model stable homotopy one-types.
