Derived mapping spaces of $\infty$-categories
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908535601758208 |
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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 |