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
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30 septembre à l'UCLouvain |
Zurab Janelidze (Stellenbosch University) |
Do torsion theories form a 2-torsion theory? |
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23 septembre à l'UCLouvain |
Giacomo Tendas (University of Manchester) |
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4 septembre à l'UCLouvain |
Dorette Pronk (Dalhousie University) |
The Three F's for Bicategories: Filteredness, Fibrations and Fractions
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22 avril à l'ULB |
Carla Rizzo (Palermo) |
Differential identities, matrix algebras and almost polynomial growth |
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Xabier García-Martínez (Vigo) |
A characterisation of Lie algebras and Gröbner bases for operads |
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15 avril à l'UCLouvain |
Marcelo Fiore (University of Cambridge) |
An Algebraic Combinatorial Approach to the Abstract Syntax of Opetopic Structures
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Matthew di Meglio (University of Edinburgh)
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Abelian groups are to abelian categories as Hilbert spaces are to what? |
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5 février à l'ULB |
Prof. Alan Cigoli (Università degli Studi di Torino)
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From Yoneda's additive regular spans to fibred cartesian monoidal opfibrations |
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Dr. Federico Campanini (UCLouvain) |
Building pretorsion theories from torsion theories |
2023
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4 décembre à l'UCLouvain |
Dr. Bryce Clarke (INRIA, Saclay) |
Bryce Clarke: The AWFS of twisted coreflections and delta lenses |
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13 novembre à l'UCLouvain |
Dr. Marco Abbadini |
Soft sheaf representations in Barr-exact categories |
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30 octobre à l'UCLouvain |
Lyne Moser |
Model structures for double categories |
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10 juillet à l'UCLouvain |
Workshop on Category Theory - UCLouvain and J. Hopkins | |
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9 janvier à l'UCLouvain |
Manuel Mancini |
Weak Representability of Actions of Non-Associative Algebras |
Abstacts
Logic from the enriched categorical point of view
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.