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arXiv · 2509.10288

Derived mapping spaces of $\infty$-categories

Kensuke Arakawa·Daniel Carranza·Chris Kapulkin
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Abstract

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.

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Kensuke Arakawa, Daniel Carranza, Chris Kapulkin. 2025-09-12. Derived mapping spaces of $\infty$-categories. https://arxiv.org/abs/2509.10288

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