2023/08/07 by Jaco Ruit, Ruit, Jaco
Mathematics · Medicine · #18D65 #18D70 #18N10 #18N65 #55U35 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications
paper · pdf · doi:10.48550/arxiv.2308.03583
openalex publication_date 2023/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize proarrow equipments from strict category theory to the ∞-categorical setting, introducing the concept of ∞-equipments. These are specific double ∞-categories that support an internal higher category theory. This paper explores several examples of ∞-equipments, including the prototypical example of the ∞-equipment of ∞-categories and the more general ∞-equipments of internal ∞-categories. The ultimate objective of this article is to study the basic concepts of category theory within an arbitrary ∞-equipment, such as colimits and Kan extensions.