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

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

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