homotopy hypothesis-theorem delooping hypothesis-theorem stabilization hypothesis-theorem The generalization of the bicategory Span to (∞,n)-categories: An -category of correspondences in ∞-groupoid is an (∞,n)-category whose objects are ∞-groupoids; morphisms are correspondences in ∞Grpd 2-morphisms are correspondences of correspondences (where the triangular sub-diagrams are filled with 2-morphisms in ∞Grpd which we do not display here) and so on up to n-morphisms -morphisms are equivalences..