nLab
groupoid-principal infinity-bundle

Context

Bundles

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 05:12:53. See the history of this page for a list of all contributions to it.