Kensuke Arakawa

collaborators

4 papers

math.AT2026

On the equivalence of Brantner's and Chu--Haugseng's approaches to enriched $\infty$ -operads

Kensuke Arakawa

We prove that two models of (monochromatic) enriched $\infty$ -operads, due to Brantner and Chu--Haugseng, are equivalent. We show this as a consequence of the equivalence of two mo…

math.AT2026

A Context for Manifold Calculus

Kensuke Arakawa

We develop Weiss's manifold calculus in the setting of $\infty$ -categories, where we allow the target $\infty$ -category to be any $\infty$ -category with small limits. We will estab…

math.AT2025

Cubical models of $\infty$ -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 $\infty$ -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 $\infty$ -categories, and allows us to provide a unif…

On the equivalence of Brantner's and Chu--Haugseng's approaches to enriched ∞-operads

A Context for Manifold Calculus

Cubical models of ∞-presheaves and the Bousfield-Kan formula

Derived mapping spaces of ∞-categories

On the equivalence of Brantner's and Chu--Haugseng's approaches to enriched $\infty$ -operads

Cubical models of $\infty$ -presheaves and the Bousfield-Kan formula

Derived mapping spaces of $\infty$ -categories