We will start our seminar on Thursday, January 24, in M5 at 1pm.
Harry Gindi
CartesianEnriched Quasicategories, the Isofibration theorem and Yoneda's lemma
Abstract: In Joyal's theory of quasicategories, there is a very nice characterization of the fibrant objects and the fibrations between them as the innerfibrant objects and isomorphismlifting inner fibrations respectively. Given a niceenough Reedy category C, we construct a horizontal model structure on the category of presheaves of sets on Θ[C] that shares a variant of this characterization. Moreover, given a Cartesian presentation with respect to simplicial presheaves on C, we show that the horizontal model structure Psh(Θ[C]) admits a leftBousfield localization that agrees with Rezk's model structure on sPsh(Θ[C]). It will follow by general facts about leftBousfield localization that the model fibrations between the local objects are exactly the horizontal isofibrations. We will also briefly describe the generalization of the homotopycoherent nerve and realization for these enriched Quasicategories and sketch a proof of Yoneda's lemma in this setting, if time permits.
