The concept of finite (∞,1)-category is the generalization of finite homotopy type from ∞-groupoids((∞,0)-categories) to (∞,1)-categories.
If we model (∞,1)-categories by quasicategories, then this can be made precise by saying it is equivalent to the fibrant replacement in the Joyal model structure of a simplicial set with finitely many nondegenerate simplices (in the ∞-groupoid case also: finite CW-complex).
Last revised on February 2, 2014 at 06:05:03. See the history of this page for a list of all contributions to it.