The group law of Picard stacks via matrices

TL;DR

This paper demonstrates that the 2-stack of strictly commutative Picard stacks over a site S is algebraic, establishing a 2-equivalence with the 2-stack of 2-algebras for an appropriate algebraic 2-stack theory over S.

Contribution

It introduces a new algebraic framework showing the 2-stack of Picard stacks is equivalent to a 2-stack of 2-algebras, advancing the understanding of their structure.

Findings

The 2-stack of Picard stacks is algebraic.

Establishment of a 2-equivalence with 2-algebras.

Provides a new perspective on the algebraic nature of Picard stacks.

Abstract

Let S be a site. We show that the 2-stack of strictly commutative Picard stacks over S is algebraic, i.e. it is 2-equivalent to the 2-stack of 2-algebras for an adequate algebraic 2-stack theory over S.