nLab delooping groupoid

Idea

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

• a single object,

• morphisms the elements of $G$,

• composition the group operation in $G$.

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

Related concepts

• a skeletal groupoid is a disjoint union of delooping groupoids

• pair groupoid

• looping and delooping

• pointed connected groupoid

References

For more see at

• Introduction to Topology – 2, Groupoids