Enhanced twisted arrow categories
| Autor: | García, Fernando Abellán, Stern, Walker H. |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given an $\infty$-bicategory $\mathbb{D}$ with underlying $\infty$-category $\mathcal{D}$, we construct a Cartesian fibration $\operatorname{Tw}(\mathbb{D})\to \mathcal{D} \times \mathcal{D}^{\operatorname{op}}$, which we call the enhanced twisted arrow $\infty$-category, classifying the restricted mapping category functor $\operatorname{Map}_{\mathbb{D}}:\mathcal{D}^{\operatorname{op}}\times \mathcal{D} \to \mathbb{D}^{\operatorname{op}} \times \mathbb{D} \to \operatorname{Cat}_{\infty}$. With the aid of this new construction, we provide a description of the $\infty$-category of natural transformations $\operatorname{Nat}(F,G)$ as an end for any functors $F$ and $G$ from an $\infty$-category to an $\infty$-bicategory. As an application of our results, we demonstrate that the definition of weighted colimits presented in arXiv:1501.02161 satisfies the expected 2-dimensional universal property. Comment: 35 pages |
| Databáze: | arXiv |
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