Homotopy Type Theory pointed connected groupoid > history (Rev #2, changes)

Definition

A pointed connected groupoid consists of

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

See also

• group

• groupoid

References

• Univalent Foundations Project, Homotopy Type Theory – Univalent Foundations of Mathematics (2013)
• Marc Bezem, Ulrik Buchholtz, Pierre Cagne, Bjørn Ian Dundas, and Daniel R. Grayson, Symmetry book (2021)