2023/07/14 by Lyne Moser, Moser, Lyne, Nima Rasekh +3
Mathematics · Medicine · #18N10 #18N45 #18N50 #18N65 #55U35 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications
paper · pdf · doi:10.48550/arxiv.2307.07259
openalex publication_date 2023/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide an (∞,n)-categorical version of the straightening-unstraightening construction, asserting an equivalence between the (∞,n)-category of double (∞,n-1)-right fibrations over an (∞,n)-category C and that of the (∞,n)-functors from C valued in (∞,n-1)-categories. We realize this in the form of a Quillen equivalence between appropriate model structures; on the one hand, a model structure for double (∞,n-1)-right fibrations over a generic precategory object W in (∞,n-1)-categories and, on the other hand, a model structure for (∞,n)-functors from its homotopy coherent categorification \mathfrakC W valued in (∞,n-1)-categories.