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Cubical models of -presheaves and the Bousfield-Kan formula
Kensuke Arakawa, Daniel Carranza, Chris Kapulkin
We construct the covariant and the cocartesian model structures on the slice categories of cubical sets and marked cubical sets, respectively. As an application, we derive a versio…
math.AT2025
Derived mapping spaces of -categories
Kensuke Arakawa, Daniel Carranza, Chris Kapulkin
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 unif…