Cohomology with coefficients in stacks of Picard categories

TL;DR

This paper develops a cohomology theory for topological spaces with coefficients in stacks of abelian 2-groups, establishing a 2-categorical analog of Grothendieck's theorem relating cohomology and Ext groups.

Contribution

It introduces a 2-categorical framework for cohomology with stacks of abelian 2-groups and proves a key analog of Grothendieck's theorem in this setting.

Findings

Established a cohomology theory with stacks of abelian 2-groups.

Proved a 2-categorical analog of Grothendieck's theorem.

Connected cohomology with Ext groups of stacks.

Abstract

Cohomology of a topological space with coefficients in stacks of abelian 2-groups is considered. A 2-categorical analog of the theorem of Grothendieck is proved, relating cohomology of the space with coefficients in a 2-stage spectrum and the Ext groups of appropriate stacks.