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

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Contents

Context

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

(∞,1)-topos theory

structures in a cohesive (∞,1)-topos

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

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.

Last revised on April 14, 2015 at 14:50:45. See the history of this page for a list of all contributions to it.