nLab
delooping groupoid

Contents

Context

Category 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

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

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

References

For more see at

Last revised on April 28, 2021 at 16:13:27. See the history of this page for a list of all contributions to it.