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Add to My Calendar

Responsabili:

Federica Galluzzi  ed  Elena Martinengo
 

Nel calendario si indicano i seminari di geometria algebrica e altre attività di interesse, organizzate dall'Università e dal Politecnico di Torino.

Evento

Titolo: Accessibility and presentability in 2-categories (Part I and Part II)
Quando: 15/11/2018 - 15:00 to 16/11/2018 - 00:00
Dove: Palazzo Campana - TORINO
Aula: Aula 4
Relatore: Fosco Loregian
Afferenza: Max Planck Institute for Mathematics, Bonn
Locandina: Locandina

Descrizione:

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/1804.08710.
The first talk is an introduction to the subject while the second one 
goes into the detailes of the preprint.

Sede

Sede: Palazzo Campana - Sito web
Indirizzo: Via Carlo Alberto 10
CAP: 10123
Città: TORINO