nLab pointed connected groupoid

Contents

Context

Group Theory

(,1)(\infty,1)-Category theory

Contents

Definition

A pointed connected groupoid is a groupoid that is pointed and connected.

Under the looping and delooping-equivalence, this is equivalently the delooping groupoid of a group.

In homotopy type theory

In homotopy type theory, a pointed connected groupoid consists of

  • A type GG
  • A basepoint e:Ge:G
  • A 0-connector
    κ 1: f:G𝟙 a:𝟙isContr([fiber(f,a)] 0)\kappa_1:\prod_{f:G \to \mathbb{1}} \prod_{a:\mathbb{1}} \mathrm{isContr}(\left[\mathrm{fiber}(f, a)\right]_{0})
  • A 1-truncator:
    τ 2:isGroupoid(G)\tau_2:\mathrm{isGroupoid}(G)

See also

References

Last revised on June 9, 2022 at 12:32:03. See the history of this page for a list of all contributions to it.