Homotopy Type Theory infinity-group > history (Rev #1)

Definition

An $\infty$-group or pointed connected type consists of

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

See also

• group

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)