Geodesic
Enhanced twisted arrow categories
Theory and applications of categories, Tome 39 (2023), pp. 98-149

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Given an ∞-bicategory D with underlying ∞-category D_0, we construct a Cartesian fibration Tw(D) --> Tw(D_0) x D_0^op, which we call the enhanced twisted arrow ∞-category, classifying the restricted mapping category functor Map_D:D_0^op x D_0 --> D^op \times D --> Cat_∞. With the aid of this new construction, we provide a description of the ∞-category of natural transformations Nat(F,G) as an end for any functors F and G from an ∞-category to an ∞-bicategory. As an application of our results, we demonstrate that the definition of weighted colimits studied by Gepner-Haugseng-Nikolaus satisfies the expected 2-dimensional universal property.

Publié le :
Classification : 18N10, 18N60, 18N65
Keywords: (∞, 2)-category, twisted arrow category, natural transformation, weighted colimit 
@article{TAC_2023_39_a3,
     author = {Fernando Abell\'an Garc{\'\i}a and Walker H. Stern},
     title = {Enhanced twisted arrow categories},
     journal = {Theory and applications of categories},
     pages = {98--149},
     publisher = {mathdoc},
     volume = {39},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a3/}
}
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Fernando Abellán García; Walker H. Stern. Enhanced twisted arrow categories. Theory and applications of categories, Tome 39 (2023), pp. 98-149. http://geodesic.mathdoc.fr/item/TAC_2023_39_a3/