nLab omega-groupoid

Idea

An $\omega$-groupoid is an ∞-category (see there for more details) in which all k-morphisms for all $k \in \mathbb{N}$ are equivalences.

This is also called an ∞-groupoid. In the literature the term “$\omega$-groupoid” is usually reserved for algebraic models instead of geometric models.

How strict the $\omega$-category and the inverses must be can vary. Somes authors that use the term ‘$\omega$-groupoid’ mean strict ∞-groupoid by default and speak of weak $\omega$-groupoid otherwise.

Related concepts

• groupoid, 2-groupoid, 3-groupoid, n-groupoid

• Grothendieck-Maltsiniotis omega-groupoid

• opetopic type theory