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.