March 5, 2020 | 2:30pm | Kent State University, Mathematical Sciences Building 115

Speaker: Amit Sharma, Kent State University

Title: Picard Groupoids and Gamma-Categories

Abstract

In this talk we will describe a construction of a symmetric monoidal closed model category of coherently commutative Picard groupoids. We will then construct another model category structure on the category of (small) permutative categories whose
fibrant objects are (permutative) Picard groupoids. We will go on to show that that the Segal′s nerve functor induces a Quillen equivalence between the two aforementioned model categories. This result implies
the classical result that Picard groupoids model stable homotopy one-types.