Kensuke Arakawa

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20232026

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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…

Universal Properties of Variations of the Little Cubes Operads

The Grothendieck Construction for ∞-Categories Fibered over Categorical Patterns

Classification diagrams of simplicial categories

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