Segal space

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 {{harvtxt|Rezk|2001}} as models for (∞, 1)-categories.