Kensuke Arakawa

activity

20232026

collaborators

10 papers

math.CT2026

Hammock localization via Segal animae

Kensuke Arakawa, Bastiaan Cnossen

We give a short, conceptual account of Dwyer--Kan's hammock localization in the setting of $\infty$ -categories. Starting from Mazel-Gee's formula for localization via the relative…

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.CT2026

On the equivalence of two approaches to multiplicative homotopy theories

Kensuke Arakawa

We study the relation of two frameworks for multiplicative homotopy theories: Presentably symmetric monoidal $\infty$ -categories and combinatorial symmetric monoidal model categori…

math.CT2025

A short proof of the universality of the relative Rezk nerve

Kensuke Arakawa, Bastiaan Cnossen

We give a concise, conceptual proof of the universality of the relative Rezk nerve, due to Mazel-Gee.

math.CT2025

Monoidal Relative Categories Model Monoidal $\infty$ -Categories

Kensuke Arakawa

We prove that the homotopy theory of monoidal relative categories is equivalent to that of monoidal $\infty$ -categories, and likewise in the symmetric monoidal setting. As an appli…

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.CT2024

The Grothendieck Construction for $\infty$ -Categories Fibered over Categorical Patterns

Kensuke Arakawa

We show how to treat families of $\infty$ -categories fibered in categorical patterns (e.g., $\infty$ -operads and monoidal $\infty$ -categories) in terms of fibrations by relativizin…

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…

Hammock localization via Segal animae

Relative dendroidal Rezk nerve and applications

On the equivalence of two approaches to multiplicative homotopy theories

A short proof of the universality of the relative Rezk nerve

Monoidal Relative Categories Model Monoidal ∞-Categories

Universal Properties of Variations of the Little Cubes Operads

The Grothendieck Construction for ∞-Categories Fibered over Categorical Patterns

Classification diagrams of simplicial categories

Classification Diagrams of Marked Simplicial Sets

Homotopy Limits and Homotopy Colimits of Chain Complexes

Monoidal Relative Categories Model Monoidal $\infty$ -Categories

The Grothendieck Construction for $\infty$ -Categories Fibered over Categorical Patterns