Higher category theory
higher category theory
Extra properties and structure
An -groupoid is an ω-category (see there for more details) in which all k-morphisms for all are equivalences.
This is also called an ∞-groupoid. In the literature the term ”-groupoid” is usually reserved for algebraic models instead of geometric models.
How strict the -category and the inverses must be can vary. Somes authors that use the term ‘-groupoid’ mean strict ω-groupoid by default and speak of weak -groupoid otherwise.
Revised on March 10, 2014 00:52:02
by Urs Schreiber