∞ groupoid

In category theory, a branch of mathematics, an ∞-groupoid is an abstract homotopical model for topological spaces. One model uses Kan complexes which are fibrant objects in the category of simplicial sets (with the standard model structure). It is an ∞-category generalization of a groupoid, a category in which every morphism is an isomorphism.

The homotopy hypothesis states that ∞-groupoids are spaces.