Title: Developing a library of formalized mathematics from a univalent point of view Abstract: The agda-unimath project started in November 2021, at a meeting called Univalent Foundations for Daily Applications. At this meeting, I proposed to formalize the Symmetry book project, in which group theory is studied from the perspective that symmetries are identifications in […]
Title: Weak homotopy types of finite spaces Abstract: Can you construct an example of a topological space with only 4 points whose fundamental group is isomorphic to the group of integers Z? Upon first glance, our intuitions about finite subspaces of R^n would suggest that a space with finitely many points cannot admit homotopically interesting […]
Title: Double Categories Abstract: This talk will give an introduction to double categories, double pseudofunctors, companions, conjoints, and some of their properties together with interesting examples and applications.
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 […]