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Pré-Publication, Document De Travail Année : 2020

Fibrations and lax limits of $(\infty,2)$-categories

Andrea Gagna
  • Fonction : Auteur
Edoardo Lanari
  • Fonction : Auteur

Résumé

We study four types of (co)cartesian fibrations of $(\infty)$-bicategories over a given base $\mathcal{B}$, and prove that they encode the four variance flavors of $\mathcal{B}$-indexed diagrams of $\infty$-categories. We then use this machinery to set up a general theory of 2-(co)limits for diagrams valued in an $\infty$-bicategory, capable of expressing lax, weighted and pseudo limits. When the $\infty$-bicategory at hand arises from a model category tensored over marked simplicial sets, we show that this notion of 2-(co)limit can be calculated as a suitable form of a weighted homotopy limit on the model categorical level, thus showing in particular the existence of these 2-(co)limits in a wide range of examples.

Dates et versions

hal-03052242 , version 1 (10-12-2020)

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Citer

Andrea Gagna, Yonatan Harpaz, Edoardo Lanari. Fibrations and lax limits of $(\infty,2)$-categories. 2020. ⟨hal-03052242⟩
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