#
nLab

delooping groupoid

Contents
### Context

#### Category theory

**category theory**

## Concepts

## Universal constructions

## Theorems

## Extensions

## Applications

#### 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

For $G$ a group, there is a groupoid $(G \rightrightarrows \ast)$ with

This may be understood as the “delooping” of $G$ in the ambient (infinity,1)-topos, and is, as such, naturally denoted $\mathbf{B}G$.

## References

For more see at

Last revised on April 28, 2021 at 16:13:27.
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