Title: Directed univalence and the Yoneda embedding for synthetic (∞,1)-categoriesAbstract: I'll present recent advances in synthetic (∞,1)-category theory, more specifically a modal extension of Riehl--Shulman's simplicial homotopy type theory. This includes the construction of the univeral left fibration, the Yoneda embedding and Yoneda lemma, a study of cofinal functors, Quillen's Theorem A, and first steps in […]