We show how to treat families of ∞-categories fibered in categorical patterns (e.g., ∞-operads and monoidal ∞-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 ∞-categories fibered in categorical patterns.
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Kensuke Arakawa (2024) studied this question.
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