Kensuke Arakawa

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20232026

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5 papers · 1 filter

math.AT2026

Relative dendroidal Rezk nerve and applications

Kensuke Arakawa, Victor Carmona, Francesca Pratali

We extend the dendroidal Rezk nerve to the setting of relative $\infty$ -operads. Our main theorem relates it to localization of $\infty$ -operads, generalizing a theorem of Mazel-Ge…

math.AT2024

Universal Properties of Variations of the Little Cubes Operads

Kensuke Arakawa

Given a map $B \to B Top (n)$ of spaces, one can define a version $E_{B}$ of the little cubes operad, whose construction is due to Lurie. We show that $\mathbb{E}_{B…

math.AT2024

Classification diagrams of simplicial categories

Kensuke Arakawa

We show that the classification diagram of a relative $\infty$ -category arising from a relative simplicial category is equivalent to the levelwise nerve. Applications include the c…

math.AT2023

Classification Diagrams of Marked Simplicial Sets

Kensuke Arakawa

We prove that the classification diagram functor from the category of marked simplicial sets to the category of bisimplicial sets carries cartesian equivalences to Rezk equivalence…

math.AT2023

Homotopy Limits and Homotopy Colimits of Chain Complexes

Kensuke Arakawa

We give a formula for homotopy limits and homotopy colimits of diagrams of chain complexes using the cobar and bar constructions, also known as the Bousfield--Kan formula. Along th…