A relative 2-nerve
| Autor: | Walker H. Stern, Fernando Abellán García, Tobias Dyckerhoff |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Functor bicategories 010102 general mathematics Context (language use) Mathematics - Category Theory 18D30 18E35 18G55 relative nerve 01 natural sciences Mathematics::Algebraic Topology 18G30 Grothendieck construction Mathematics::Category Theory 0103 physical sciences 010307 mathematical physics Geometry and Topology Mathematics - Algebraic Topology 0101 mathematics Equivalence (measure theory) Mathematics |
| Zdroj: | Algebr. Geom. Topol. 20, no. 6 (2020), 3147-3182 |
| Popis: | In this work, we introduce a 2-categorical variant of Lurie's relative nerve functor. We prove that it defines a right Quillen equivalence which, upon passage to $\infty$-categorical localizations, corresponds to Lurie's scaled unstraightening equivalence. In this $\infty$-bicategorical context, the relative 2-nerve provides a computationally tractable model for the Grothendieck construction which becomes equivalent, via an explicit comparison map, to Lurie's relative nerve when restricted to 1-categories. Comment: 30 pages, 1 figure, v2:minor revisions, v3: final version accepted for publication in Algebr. Geom. Topol |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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