A characterization of simplicial localization functors

2010/12/07 by Clark Barwick, Barwick, C., D Kan +1 · 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.1012.1540

openalex publication_date 2010/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize simplicial localization functors among relative functors from relative categories to simplicial categories as any choice of homotopy inverse to the delocalization functor of Dwyer and the second author.

Cited by

• Relative categories: Another model for the homotopy theory of homotopy theories
• Algebraic K-theory of finitely projective modules on 𝔼_∞-rings

Related

• Revisiting function complexes and simplicial localisation
• Classification Diagrams of Marked Simplicial Sets
• Deligne Localized Functors
• Replacing functors with enriched ones
• Simplicial localization of homotopy algebras over a prop