nLab
nonabelian groupoid cohomology

Skip the Navigation Links | Home Page | All Pages | Recently Revised | Authors | Feeds | Export |

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Edit this sidebar

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 of groups G.

Examples

Atiyah Lie groupoid

The Atiyah Lie groupoid At(P)→Π(X) of a principal bundle P→X is the extension of Π(X) classified by the nonabelian groupoid cocycle Π(X)→BAUT(G) coming from a connection on P.

Revised on January 11, 2010 23:45:35 by David Roberts (203.24.207.198)
Edit | Back in time (2 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: nonabelian cohomology, torsor, abelian sheaf cohomology, cohomology, twisting function, bundle gerbe, local system, constant infinity-stack, motivation for sheaves, cohomology and higher stacks, Eckmann-Hilton duality, principal bundle, vector bundle, string structure, Eilenberg-Mac Lane spectrum, tmf, gerbe, Hochschild-Serre spectral sequence, fiber sequence, principal 2-bundle, principal infinity-bundle, group cohomology, twisted cohomology, generalized (Eilenberg-Steenrod) cohomology, generalized cohomology, Sweedler coring, algebraic K-theory, bialgebra cocycle, chain homology and cohomology, K-theory, Karoubi K-theory, cup product, concordance, twisted bundle, bundle gerbe module, twisted K-theory, topological K-theory, Bredon cohomology, fiber bundle, singular cohomology, cohomology - contents, equivariant cohomology, A Survey of Elliptic Cohomology, elliptic cohomology, line bundle, cohomology ring, A Survey of Elliptic Cohomology - cohomology theories, de Rham complex, cobordism cohomology theory, reduced cohomology, multiplicative cohomology theory, Fivebrane structure, spin structure, orientation, A Survey of Elliptic Cohomology - formal groups and cohomology, de Rham theorem, Gromov-Witten invariants, geometric model for elliptic cohomology, Brown representability theorem, cochain on a simplicial set, A Survey of Elliptic Cohomology - elliptic curves, nonabelian Hodge theory, string 2-group, string group, Fivebrane group, Lie algebra cohomology, fivebrane 6-group, nonabelian groupoid cohomology, A Survey of Elliptic Cohomology - A-equivariant cohomology, Lie algebra extension, Hodge theory, motive, A Survey of Elliptic Cohomology - the derived moduli stack of derived elliptic curves, topological chiral homology, etale cohomology, motivic cohomology, nonabelian Lie algebra cohomology, group extension, nonabelian group cohomology, monadic descent, cocycle, Chern character, lifting gerbe, groupoid cohomology, cohomology of a category, higher monadic descent, Liouville cocycle, bibundle, infinity-Lie algebra cohomology, circle bundle, relative cohomology, characteristic class, Hochschild cohomology, cyclic cohomology, constant sheaf, locally constant infinity-stack, constant stack, crystalline cohomology, Maslov index, simplicial principal bundle, G-structure, fiber integration, Thom isomorphism, orientation in generalized cohomology, ordinary cohomology, Poincare lemma, syntomic cohomology, Floer homology, Witten genus, harmonic form, differential cobordism cohomology, cohomological descent, groupal model for universal principal infinity-bundles, universal coefficient theorem, groupoid principal bundle, associated infinity-bundle, hypercohomology, universal principal infinity-bundle, Pontryagin class, secondary characteristic class, Lie group cohomology, bundle 2-gerbe, nonabelian bundle gerbe, nonabelian bundle 2-gerbe, principal 3-bundle, Chern class, vielbein, Stokes theorem, differential characteristic class, cohomology with constant coefficients, locally constant stack, Whitehead principle of nonabelian cohomology, quantum sheaf cohomology, Dixmier-Douady class, n-vector bundle, KK-theory, coboundary, cohomological dimension, cohomology operation, infinity-gerbe, discrete torsion, cohomology localization, E-theory, Deligne conjecture, Gerstenhaber-Schack cohomology, Gelfand-Fuks cohomology, Parametrized Homotopy Theory, fundamental class, (infinity,1)-vector bundle, twisted spin structure, Stiefel-Whitney class, contents of contents, 2-gerbe, twisted spin^c structure, universal characteristic class, Euler class, Yang-Mills instanton Floer homology, spin^c structure, integral Stiefel-Whitney class, Bockstein homomorphism, cohomology in a local net of observables, 2-framing, cohomology of operads, twisted Wu structure, double cover, Hodge conjecture, first Chern class, universal principal bundle, Mayer-Vietoris sequence, intersection pairing, Wu class, Grothendieck-Riemann-Roch theorem, reduction and lift of structure groups, Steenrod square, integral Wu structure, string^c 2-group, K-theory of a bipermutative category, obstruction, twisted smooth cohomology in string theory, Kadeishvili's theorem, canonical bundle, Theta characteristic, compactly supported cohomology, KR-theory, ring extension, local coefficient bundle, fiber infinity-bundle, K-theory of a permutative category, cochain, infinity-group extension, Hilbert's Theorem 90, groupoid-principal infinity-bundle, Hodge structure, long exact sequence in homology, Hodge theorem, Galois cohomology, suspension isomorphism, Massey product, k-invariant, 2-vector bundle, line 2-bundle, instanton sector, cofiber sequence, level (Chern-Simons theory), centrally extended groupoid, operator K-theory, cohomological integration, Poisson cohomology, Fredholm module, K-homology