2020/09/24 by Fernando Abellán García, García, Fernando Abellán, Walker H. Stern +1
Mathematics · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2009.11969
openalex publication_date 2020/09/24 · openalex created_date 2020/10/01 · openalex updated_date 2026/07/28
Given an ∞-bicategory \mathbbD with underlying ∞-category D, we construct a Cartesian fibration Tw(\mathbbD)→ D × Dop, which we call the enhanced twisted arrow ∞-category, classifying the restricted mapping category functor Map_\mathbbD:Dop× D → \mathbbDop × \mathbbD → 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 presented in arXiv:1501.02161 satisfies the expected 2-dimensional universal property.