homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
n-category = (n,n)-category
n-groupoid = (n,0)-category
In any ambient category or -category that admits a notion of colimit or weak colimit, a simplicial resolution of an object is a simplicial object such that it realizes as a colimit
The term is also used for a Reedy fibrant replacement of a constant simplicial object in a model category; see also resolution.
Simplicial resolutions in the context of presentable (infinity,1)-categories are discussed in section 6.1.4 of
(below lemma 6.1.4.3)