nLab
nonabelian groupoid cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

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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 January 11, 2010 at 23:45:35. See the history of this page for a list of all contributions to it.