Segal space
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In mathematics, a Segal space is a simplicial space satisfying some pullback conditions, making it look like a homotopical version of a category. More precisely, a simplicial set, considered as a simplicial discrete space, satisfies the Segal conditions if and only if it is the nerve of a category. The condition for Segal spaces is a homotopical version of this.
Complete Segal spaces were introduced by Rezk (2001) as models for (∞, 1)-categories.
- Rezk, Charles (2001), "A model for the homotopy theory of homotopy theory", Transactions of the American Mathematical Society, 353 (3): 973–1007, doi:, ISSN , MR