Title: Cartesian Fibrations and Representability,
Abstract: In higher category theory, we use fibrations to model presheaves. In this
paper we introduce a new method to build such fibrations. Concretely, for
suitable reflective subcategories of simplicial spaces, we build fibrations
that model presheaves valued in that subcategory. Using this we can build
Cartesian fibrations, but we can also model presheaves valued in Segal spaces.
Additionally, using this new approach, we define representable Cartesian
fibrations, generalizing representable presheaves valued in spaces, and show
they have similar properties.