Talk 1) November 15, 3:00 pm - 4:30 pm (Aula 4).
Title: Accessibility and presentability in 2-categories (PART I).
Talk 2) November 16, 3:00 pm - 4:30 pm (Aula 4).
Title: Accessibility and presentability in 2-categories (PART II).
Abstract: We outline a definition of accessible and presentable objects
in a 2-category endowed with a Yoneda structure, this perspective
suggests a unified treatment of many "Gabriel-Ulmer like" theorems (like
the classical Gabriel-Ulmer representation for locally presentable
categories, Giraud theorem, and Gabriel-Popescu theorem), asserting how
presentable objects arise as reflections of generating ones. In a Yoneda
structure whose underlying presheaf construction is P, two
non-equivalent definitions of presentability for A in K can be given: in
the most interesting, it is generally false that all presheaf objects
are presentable, this leads to the definition of a Gabriel-Ulmer
structure, i.e. a Yoneda structure rich enough to concoct Gabriel-Ulmer
duality and to make this asymmetry disappear. We end the paper with a
roundup of examples, involving classical (set-based and enriched), low
dimensional and higher dimensional category theory.
These talks are based on the preprint: https://arxiv.org/abs/1804.087
The first talk is an introduction to the subject while the second one
goes into the detailes of the preprint.