Séminaire de théorie des catégories

Louvain-La-Neuve

Le Séminaire de Théorie des Catégories a lieu en alternance à l'UCLouvain, à l'ULB et à la VUB. 

Où?

UCLouvain : Institut de recherche en mathématique et physique (Chemin du Cyclotron 2, 1348 Louvain-la-Neuve)

ULB : Département de Mathématique (Campus de la Plaine, Boulevard du Triomphe, 1050 Bruxelles)

VUB : Vakgroep Wiskunde (bâtiment G, 6ème étage, sur le campus d'Etterbeek, Boulevard de la Plaine 2, 1050 Bruxelles)

Organisateurs 

Université catholique de Louvain : Marino Gran, Tim Van der Linden, Enrico Vitale

Université libre de Bruxelles: Joost Vercruysse

Vrije Universiteit Brussel : Stefaan Caenepeel, Mark Sioen

D'autres exposés en lien avec la théorie des catégories sont organisés dans le cadre du Seminar on quantum groups, Hopf algebras and monoidal categories.

Exposés

2024

30 septembre

à l'UCLouvain

Zurab Janelidze (Stellenbosch University)

Do torsion theories form a 2-torsion theory?

23 septembre

à l'UCLouvain

Giacomo Tendas (University of Manchester)

Logic from the enriched categorical point of view

4 septembre

à l'UCLouvain

Dorette Pronk (Dalhousie University)

The Three F's for Bicategories: Filteredness, Fibrations and Fractions

22 avril 

à l'ULB

Carla Rizzo (Palermo)
 

Differential identities, matrix algebras and almost polynomial growth

 

Xabier García-Martínez (Vigo)

A characterisation of Lie algebras and Gröbner bases for operads

15 avril

à l'UCLouvain

Marcelo Fiore (University of Cambridge)

An Algebraic Combinatorial Approach to the Abstract Syntax of Opetopic Structures

 

 

Matthew di Meglio (University of Edinburgh)

 

Abelian groups are to abelian categories as Hilbert spaces are to what?

5 février 

à l'ULB

Prof. Alan Cigoli (Università degli Studi di Torino)

 

From Yoneda's additive regular spans to fibred cartesian monoidal opfibrations

                                               

Dr. Federico Campanini (UCLouvain)
 

Building pretorsion theories from torsion theories

2023

 

4 décembre

à l'UCLouvain

Dr. Bryce Clarke (INRIA, Saclay) 

 

Bryce Clarke: The AWFS of twisted coreflections and delta lenses

 

13 novembre

à l'UCLouvain

Dr. Marco Abbadini
(University of Birmingham)

Soft sheaf representations in Barr-exact categories

30 octobre

à l'UCLouvain 

Lyne Moser
(University of Regensburg)

Model structures for double categories 

10 juillet 

à l'UCLouvain 

 

Workshop on Category Theory - UCLouvain and J. Hopkins

9 janvier

à l'UCLouvain                                    

Manuel Mancini
(University of Palermo)                                                              

Weak Representability of Actions of Non-Associative Algebras                                                                                                                   
 

 

Abstacts

Logic from the enriched categorical point of view - Giacomo Tendas

In logic, regular theories are those whose axioms are built using only equations, relation symbols, conjunctions, and existential quantification. The categories of models of such theories have been widely studied and characterised in purely category theoretical terms through the notions of exact and abielian category, and of injectivity class; I will recall these during the talk.

When moving to the context of categories enriched over a base V, corresponding notions of "exact V-category" and "V-injectivity class" have been studied by several authors, but no enriched notion of regular logic was considered in the literature before. The aim of this talk, which is based on joint work with Rosicky, is to fill this gap by introducing a notion of "enriched regular logic" that interacts well with the category theoretical counterparts mentioned above. Among others, we'll see examples from the additive, differentially graded, and 2-categorical setting.

Do torsion theories form a 2-torsion theory? - Zurab Janelidze

The category of 1-categories forms a 2-category. Recently, I showed that a suitable category of Puppe exact categories forms a 2-category that satisfies 2-dimensional counterparts of the axioms of a Puppe exact category (joint work in progress with Ülo Reimaa).

1-cells in this 2-category are to be called Serre functors, as they are closely linked with Serre subcategory inclusions and Serre quotients of abelian categories, and include those as special cases. This is a promising example of a potentially general phenomenon: a 2-category of 1-categories defined by an algebraic exactness property exhibits a 2-dimensional counterpart of the same exactness property.

In this talk we discuss work in progress on showing that a similar phenomenon could be exhibited for algebraically structured categories: we make first steps in showing that the 2-category of categories equipped with a torsion theory itself has a 2-dimensional torsion theory. What is common to both 2-dimensional situations is the use of the same and the usual notions of 2-zero object, 2-kernels and 2-cokernels.