Completions and DK-equivalences of Θ_n-spaces

2025/03/03 by Miika Tuominen, Tuominen, Miika
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2503.01687

openalex publication_date 2025/03/03 · openalex created_date 2025/10/19 · openalex updated_date 2026/08/03

Abstract

We establish Rezk completion functors for Θ_n-spaces with respect to each and all of the completeness conditions. As a consequence, we obtain a characterization completeness of Segal Θ_n-spaces as locality with respect to higher-dimensional Dwyer-Kan equivalences.

Related

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• Introduction to Complete Segal Spaces
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• Retractive spaces and Bousfield-Kan completions
• In the category of relative categories the Rezk equivalences are exactly the DK-equivalences