Homotopy hypothesis

Short description: Hypothesis that the ∞-groupoids are equivalent to the topological spaces

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

• Pursuing Stacks
• N-group (category theory)
• Quasi-category

References

• John Baez, The Homotopy Hypothesis
• Grothendieck, Alexander (2021). Pursuing Stacks. 
• Lurie, Jacob (2009). Higher Topos Theory (AM-170). Princeton University Press. ISBN 9780691140490. 

External links

• homotopy hypothesis in nLab
• What is the mistake in the proof of the Homotopy hypothesis by Kapranov and Voevodsky?
• Jacob Lurie's Home Page