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Calculus of Fractions for Quasicategories

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arxiv 2306.02218 v2 pith:NJCKZDQE submitted 2023-06-04 math.AT math.COmath.CT

Daniel Carranza , Chris Kapulkin , Zachery Lindsey This is my paper · ORCID
classification math.ATmath.COmath.CT
keywords calculusfractionslocalizationmarkedquasicategoriesquasicategoryappropriatecarry
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We describe a generalization of Gabriel and Zisman's Calculus of Fractions to quasicategories, showing that the two essentially coincide for the nerve of a category. We then prove that the marked Ex-functor can be used to compute the localization of a marked quasicategory satisfying our condition and that the appropriate (co)completeness properties of the quasicategory carry over to its localization.

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  1. Homotopical presentation of categories

    math.CT 2024-11 conditional novelty 6.0 of 10

    A finite-limit-preserving functor with an admissible lifting property yields a Quillen equivalence presenting the universal model category of the target.

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