homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
n-category = (n,n)-category
n-groupoid = (n,0)-category
A Gray-group is a semistrict version of a 3-group: it is a 3-group whose delooping is a one-object Gray groupoid.
Gray-groups are modeled by 2-crossed module in analogy to how strict 2-groups are modeled by crossed modules.