Complete Segal Objects

2018/05/09 by Nima Rasekh, Rasekh, Nima · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1805.03561

openalex publication_date 2018/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define complete Segal objects, which play the role of internal higher category objects. Then we study them using representable Cartesian fibrations, in particular defining adjunctions and limits of complete Segal objects. Finally we use Segal objects to define univalence in a locally Cartesian closed category that is not presentable and generalize some previous results to the non-presentable setting.

Citations

• The Simplicial Model of Univalent Foundations (after Voevodsky)

Cited by

• A Theory of Elementary Higher Toposes

Related

• Introduction to Complete Segal Spaces
• Cartesian Fibrations and Representability
• Cartesian Fibrations of Complete Segal Spaces
• A Model for the Higher Category of Higher Categories
• Segal objects and the Grothendieck construction