Kensuke Arakawa

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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.AT2026

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…

math.AT2025

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.AT2025

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…