2024/06/14 by Hadrian Heine, Heine, Hadrian
Mathematics · Medicine · #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Vascular Malformations Diagnosis and Treatment
paper · pdf · doi:10.48550/arxiv.2406.09832
openalex publication_date 2024/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend Lurie's definition of enriched ∞-categories to notions of left enriched, right enriched and bienriched ∞-categories, which generalize the concepts of closed left tensored, right tensored and bitensored ∞-categories and share many desirable features with them. We use bienriched ∞-categories to endow the ∞-category of enriched functors with enrichment that generalizes both the internal hom of the tensor product of enriched ∞-categories when the latter exists, and the free cocompletion under colimits and tensors. As an application we construct enriched Kan-extensions from operadic Kan-extensions, compute the monad for enriched functors, prove an end formula for morphism objects of enriched ∞-categories of enriched functors and a coend formula for the relative tensor product of enriched profunctors and construct transfer of enrichment from scalar extension of presentably bitensored ∞-categories. In particular, we develop an independent theory of enriched ∞-categories for Lurie's model of enriched ∞-categories.