Coskeletality and the higher Segal conditions

2026/07/27 by Philip Hackney
Mathematics · #math.AT #math.CT

paper · pdf

Abstract

A simplicial set is d-Segal if and only if it is (d+1)-coskeletal and satisfies the d-Segal condition in the two lowest relevant simplicial dimensions.

Citations

• Higher Segal spaces and partial groups
• Cyclic polytopes, orientals, and correspondences: some aspects of higher Segal spaces
• Higher Segal structures in algebraic K-theory
• 2-Segal sets and the Waldhausen construction

Related

• Higher Segal spaces and partial groups
• Segal's multisimplicial spaces
• Lawvere's fourth open problem: Levels in the topos of symmetric simplicial sets
• The edgewise subdivision criterion for 2-Segal objects
• Segalification and the Boardman-Vogt tensor product