2019/02/14 by Viktoriya Ozornova, Ozornova, Viktoriya, Martina Rovelli +1
Mathematics · Medicine · #18D05 #55U10 #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.1902.05524
openalex publication_date 2019/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the homotopy theory of strict 2-categories embeds in that of (∞,2)-categories in the form of 2-precomplicial sets. More precisely, we construct a nerve-categorification adjunction that is a Quillen pair between Lack's model structure for 2-categories and Riehl-Verity's model structure for 2-complicial sets. Furthermore, we show that Lack's model structure is transferred along this nerve and that the nerve is homotopically fully faithful.