omega-groupoid

- homotopy hypothesis-theorem
- delooping hypothesis-theorem
- periodic table
- stabilization hypothesis-theorem
- exactness hypothesis
- holographic principle

- (n,r)-category
- Theta-space
- ∞-category/∞-category
- (∞,n)-category
- (∞,2)-category
- (∞,1)-category
- (∞,0)-category/∞-groupoid
- n-category = (n,n)-category
- 2-category, (2,1)-category
- 1-category
- 0-category
- (?1)-category?
- (?2)-category?

- n-poset = (n-1,n)-category
- n-groupoid = (n,0)-category

- categorification/decategorification
- geometric definition of higher category
- algebraic definition of higher category
- stable homotopy theory

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.

Last revised on October 24, 2018 at 16:30:17. See the history of this page for a list of all contributions to it.