The Derived Mapping Space Lemma generalizes mapping spaces in infinity-categories, highlighting localization conditions.
We prove the Derived Mapping Space Lemma, which generalizes the central theorem of Cisinski's work on calculus of fractions for ∞-categories, and allows us to provide a unified framework for analyzing mapping spaces in localizations of (∞-)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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Arakawa et al. (2025) studied this question.
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