Homotopy hypothesis
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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 also
References
- John Baez, The Homotopy Hypothesis
- Grothendieck, Alexander (2021). "Pursuing Stacks". arXiv:2111.01000 [math.CT].
- Lurie, Jacob (2009). Higher Topos Theory (AM-170). Princeton University Press. ISBN 9780691140490. JSTOR j.ctt7s47v.