(see also Chern-Weil theory, parameterized homotopy theory)
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
The generalization of a $G$-principal ∞-bundle over an ∞-group $G$ as $G$ is generalized to a groupoid object in an (∞,1)-category.
For $\mathbf{H}$ an (∞,1)-topos and $\mathcal{G}_\bullet \in Grp_\infty(\mathbf{H})$ a groupoid object in an (∞,1)-category, a $\mathcal{G}_\bullet$-principal $\infty$-bundle over $X$ is
a morphism $P \to X$
equipped with an anchor $a \colon P \to \mathcal{G}_0$ and a groupoid ∞-action of $\mathcal{G}_\bullet$ on $(P,a)$ over $X$;
such that $P \to X \simeq (P//\mathcal{G})$ 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.