nLab fundamental 2-groupoid

Contents

Context

2-category theory

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

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

Idea

Given a well-bahaved topological space XX, its fundamental 2-groupoid is the 2-groupoid whose

This may equivalently be understood as:

At least if XX admits the structure of a CW-complex, its fundamental 2-groupoid captures the underlying 2-truncated weak homotopy type (the homotopy 2-type).

References

Original discussion of the fundamental 2-groupoid of Hausdorff topological spaces as a strict 2-groupoid (Grpd-enriched category):

and as a weak 2-groupoid:

Created on January 19, 2023 at 11:35:52. See the history of this page for a list of all contributions to it.