Derived mapping spaces of $\infty$-categories

Fuente: arXiv
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Hauptverfasser: Arakawa, Kensuke, Carranza, Daniel, Kapulkin, Chris
Format: Preprint
Veröffentlicht: 2025
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author Arakawa, Kensuke
Carranza, Daniel
Kapulkin, Chris
author_facet Arakawa, Kensuke
Carranza, Daniel
Kapulkin, Chris
contents We prove the Derived Mapping Space Lemma, which generalizes the central theorem of Cisinski's work on calculus of fractions for $\infty$-categories, and allows us to provide a unified framework for analyzing mapping spaces in localizations of ($\infty$-)categories. As an application, we give a sufficient condition for when a cubical or simplicial category is the localization of its underlying category at homotopy equivalences.
format Preprint
id arxiv_https___arxiv_org_abs_2509_10288
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Derived mapping spaces of $\infty$-categories
Arakawa, Kensuke
Carranza, Daniel
Kapulkin, Chris
Algebraic Topology
Category Theory
18N55, 18N60, 18N40, 55U35
We prove the Derived Mapping Space Lemma, which generalizes the central theorem of Cisinski's work on calculus of fractions for $\infty$-categories, and allows us to provide a unified framework for analyzing mapping spaces in localizations of ($\infty$-)categories. As an application, we give a sufficient condition for when a cubical or simplicial category is the localization of its underlying category at homotopy equivalences.
title Derived mapping spaces of $\infty$-categories
topic Algebraic Topology
Category Theory
18N55, 18N60, 18N40, 55U35
url https://arxiv.org/abs/2509.10288