∞-groupoid
Abstract homotopical model for topological spaces / From Wikipedia, the free encyclopedia
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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).[1] It is an ∞-category generalization of a groupoid, a category in which every morphism is an isomorphism.
The homotopy hypothesis states that ∞-groupoids are equivalent to spaces up to homotopy.[2]: 2–3 [3]