A characterization of simplicial localization functors
C. Barwick, D. M. Kan
TL;DR
This paper characterizes simplicial localization functors as homotopy inverses to a specific delocalization functor, providing a clear understanding of their role in the context of relative categories.
Contribution
It offers a precise characterization of simplicial localization functors as homotopy inverses to the Dwyer–Kan delocalization functor.
Findings
Simplicial localization functors are identified as homotopy inverses.
Provides a characterization within the framework of relative categories.
Clarifies the relationship between localization and delocalization functors.
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models