nLab
fundamental infinity-groupoid in a locally infinity-connected (infinity,1)-topos

Context

(,1)(\infty,1)-Topos Theory

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Homotopy theory

Contents

Definition

For (ΠΓLConst):HGrpd(\Pi \dashv \Gamma \dashv LConst) : \mathbf{H} \to \infty Grpd a locally ∞-connected (∞,1)-topos and XHX \in \mathbf{H} an object, we say that Π(X)\Pi(X) is the fundamental \infty-groupoid of XX in H\mathbf{H}.

Properties

Examples

References

See also

for further discussion of the smooth shape modality of cohesion (the etale homotopy type operation in the context of smooth infinity-stacks) as applied to orbifolds and étale groupoids and generally étale ∞-groupoids.

Revised on April 14, 2015 14:50:45 by Urs Schreiber (195.113.30.252)