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.
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Grothendieck's homotopyhypothesis states that the ∞-groupoids are spaces. If we model our ∞-groupoids as Kan complexes, then the homotopy types of the...
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rather evident sense. In the category of pointed spaces, fundamental in homotopy theory, the coproduct is the wedge sum (which amounts to joining a collection...
Introduction to Category Theory, ISBN 978-0521283045. Simpson, Carlos (2010). Homotopy theory of higher categories. arXiv:1001.4071. Bibcode:2010arXiv1001.4071S...
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