Segal space

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Segal space is a kind of simplicial space that satisfies certain pullback conditions, so it behaves like a category in a homotopy sense. For ordinary simplicial sets viewed as discrete spaces, the Segal condition holds exactly when the set is the nerve of a category. The Segal condition is extended to the homotopical setting by Segal spaces. Complete Segal spaces, introduced by Rezk in 2001, model (∞,1)-categories.