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

Kensuke Arakawa

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arXiv · 2404.01025

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

Kensuke Arakawa

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Abstract

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 relativizing the Grothendieck construction. As applications, we construct an analog of the universal cocartesian fibration and explain how to compute limits and colimits of $\infty$-categories fibered in categorical patterns.

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Kensuke Arakawa. 2024-04-01. The Grothendieck Construction for $\infty$-Categories Fibered over Categorical Patterns. https://arxiv.org/abs/2404.01025

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