2021/02/09 by Nima Rasekh, Rasekh, Nima
Mathematics · Medicine · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Intracranial Aneurysms: Treatment and Complications
paper · pdf · doi:10.48550/arxiv.2102.05190
Cartesian fibrations were originally defined by Lurie in the context of quasi-categories and are commonly used in (∞,1)-category theory to study presheaves valued in (∞,1)-categories. In this work we define and study fibrations modeling presheaves valued in simplicial spaces and their localizations. This includes defining a model structure for these fibrations and giving effective tools to recognize its fibrations and weak equivalences. This in particular gives us a new method to construct Cartesian fibrations via complete Segal spaces. In addition to that, it allows us to define and study fibrations modeling presheaves of Segal spaces.