Gray-groupoid

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

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

A **Gray-Groupoid** is a semistrict algebraic model for a 3-groupoid:

it is a Gray-category – a semistrict 3-category – in which every k-morphism is invertible.

Gray-groupoids are related to 2-crossed complexes and 2-crossed modules as strict 2-groupoids are related to crossed complexes.

A Gray groupoid with a single object is the delooping of a Gray group.

Revised on July 22, 2010 15:57:34
by Urs Schreiber
(87.212.203.135)