nLab nonabelian groupoid cohomology

Contents

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

Nonabelian groupoid cohomology is the nonabelian cohomology of groupoids.

This generalizes nonabelian group cohomology, which is the special case of nonabelian group cohomology for groupoids that are deloopings BG\mathbf{B}G of groups GG.

Examples

Atiyah Lie groupoid

The Atiyah Lie groupoid At(P)Π(X)At(P) \to \Pi(X) of a principal bundle PXP \to X is the extension of Π(X)\Pi(X) classified by the nonabelian groupoid cocycle Π(X)BAUT(G)\Pi(X) \to \mathbf{B} AUT(G) coming from a connection on PP.

Last revised on April 1, 2023 at 13:10:38. See the history of this page for a list of all contributions to it.