nLab groupoid-principal infinity-bundle

Contents

Context

Bundles

bundles

Context

Classes of bundles

Universal bundles

Presentations

Examples

Constructions

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

The generalization of a GG-principal ∞-bundle over an ∞-group GG as GG is generalized to a groupoid object in an (∞,1)-category.

Definition

For H\mathbf{H} an (∞,1)-topos and 𝒢 Grp (H)\mathcal{G}_\bullet \in Grp_\infty(\mathbf{H}) a groupoid object in an (∞,1)-category, a 𝒢 \mathcal{G}_\bullet-principal \infty-bundle over XX is

  • a morphism PXP \to X

  • equipped with an anchor a:P𝒢 0a \colon P \to \mathcal{G}_0 and a groupoid ∞-action of 𝒢 \mathcal{G}_\bullet on (P,a)(P,a) over XX;

  • such that PX(P//𝒢)P \to X \simeq (P//\mathcal{G}) is the corresponding quotient map.

Last revised on January 5, 2018 at 10:12:53. See the history of this page for a list of all contributions to it.