delooping groupoid (changes) in nLab

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Idea

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

• a single object,

• morphisms the elements of GG,

• composition the group operation in GG.

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.

• 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