# nLab fundamental 2-groupoid

Contents

### Context

#### 2-category theory

2-category theory

Definitions

Transfors between 2-categories

Morphisms in 2-categories

Structures in 2-categories

Limits in 2-categories

Structures on 2-categories

# Contents

## Idea

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

This may equivalently be understood as:

At least if $X$ 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.