Homotopy hypothesis

In category theory, a branch of mathematics, Grothendieck's homotopy hypothesis states that the ∞-groupoids are equivalent to the topological spaces. If we model our ∞-groupoids as Kan complexes, then the homotopy types of the geometric realizations of these sets give models for every homotopy type. It is conjectured that there are many different "equivalent" models for ∞-groupoids all which can be realized as homotopy types.