Kensuke Arakawa

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20232026

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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.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.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…

Hammock localization via Segal animae

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

The Grothendieck Construction for ∞-Categories Fibered over Categorical Patterns

Monoidal Relative Categories Model Monoidal $\infty$ -Categories

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