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Does the homotopy hypothesis suggest that other geometric objects can be expressed as higher categories?

Thank you

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What are "other geometric objects"? – SL2 Nov 7 '12 at 5:09
What is the "homotopy hypothesis"? – Joe Johnson 126 Nov 7 '12 at 5:32
@JoeJohnson126 Homotopy hypothesis. Essentially, it says that spaces up to weak equivalence = $\infty$-groupoids. – SL2 Nov 7 '12 at 5:39

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