Homotopy hypothesis


In category theory, a branch of mathematics, Grothendieck's homotopy hypothesis states that the ∞-groupoids are 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.

See alsoEdit


  • John Baez, The Homotopy Hypothesis

External linksEdit

  • homotopy hypothesis in nLab
  • What is the mistake in the proof of the Homotopy hypothesis by Kapranov and Voevodsky?