Category theory | Simplicial sets

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 iff it is the nerve of a category. The condition for Segal spaces is a homotopical version of this. Complete Segal spaces were introduced by as models for (∞, 1)-categories. (Wikipedia).

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Related pages

Pullback | Homotopy | Nerve (category theory) | Category (mathematics) | Simplicial space | Simplicial set