Hjem
Algebra
Seminar

Kategoriteori i Norge

Dagsseminar for å samle folk i Norge med forskningsaktivitet og interesser mot kategoriteori. Presentasjoner blir holdt fra ståsteder innen algebra, topologi og informatikk.

Korskirkeallmenningen
Korskirkeallmenningen
Foto/ill.:
Creative Commons Attribution-Share Alike 4.0

Hovedinnhold

For påmelding kontakt: Gunnar Fløystad, nmagf at uib.no

 

Foredragsholdere og program

  • Fernando Abellan Garcia, NTNU
  • Petter Andreas Bergh, NTNU
  • Johanne Haugland, NTNU
  • Joachim Tilsted Kristensen, UiO
  • Arvid Siqveland, Universitetet i Sørøst-Norge
  • Uwe Wolter, Universitetet i Bergen

 

Møtet holdes i seminarrom Pi i Fjerde, rom 4E15B, fjerde etasje sør, Realfagsbygget.

9.00-9.45: Johanne Haugland, NTNU

10.00-10.45: Fernando Abellan Garcia, NTNU

11.15-12.00: Joachim Tilsted Kristensen, UiO

12.00-13.30: Lunsj

13.30-14.15: Petter Andreas Bergh, NTNU

14.30-15.15: Arvid Siqveland, UiSø-Norge

15.45-16.30: Uwe Wolter, UiB

 

Foredrag

Petter Andreas Bergh, NTNU

Finite tensor categories and their cohomology

Sammendrag: Finite tensor categories are abelian categories equipped with a monoidal structure. A typical example is the module category over a group algebra, or more generally the module category over a Hopf algebra.

The total cohomology ring of the unit object is a commutative graded ring. The central conjecture in this area states that this ring is a finitely generated algebra. We discuss this conjecture and look at some recent developments.

 

Fernando Abellan Garcia, NTNU

From homotopy theory to category theory.

Sammendrag: The goal of this talk is to introduce the notion of a 1-groupoid—a 1-category where every morphism is an isomorphism—and its relation to homotopy theory. We associate to every topological space X, a groupoid –the fundamental groupoid of X. This construction suitably generalizes the fundamental group of X, a well-known invariant of  topological spaces.

I will explain how to generalize the fundamental groupoid construction to higher category theory and sketch the definition of an ∞-groupoid.

 

 

Johanne Haugland, NTNU

Geometric interpretations of (sub)categories

Sammendrag: We give an introduction to a geometric model allowing us to understand certain important categories in terms of the geometry of an associated surface. Indecomposable objects in our categories correspond to curves on the surface, while morphisms and extensions arise from intersections of curves.

We investigate how triangulations of such a surface correspond to subcategories with nice algebraic properties. This is based on joint work with Karin M. Jacobsen, Ralf Schiffler and Sibylle Schroll.

 

 

Joachim Tilsted Kristensen, UiO

Typed λ-calculi and cartesian closed categories

Sammendrag: In programming language theory and proof theory, the Curry–Howard-Lambek correspondence is the direct relationship between intuitionistic logic, computer programs and mathematical proofs. We introduce the simply typed lambda calculus and show how we can represent propositions as types and terms as objects.

We outline what this means for type systems design and we demonstrate how it can beused to verify properties of functional programs.

 

 

Arvid Siqveland, UiSø-Norge

Categorical definition of algebraic objects

Sammendrag: Vi begynner med definisjonen av representerbare funktorer på små kategorier. Dette bruker vi til å definere generelle moduli objekter.

Vi viser at noen algebraiske objekter kan defineres ved egenskapen å være et moduli for en gitt mengde elementer definert av en funktor. Eksemplene er endelige grupper, vektorrom, topologiske rom og algebraiske skjemaer. Vi avslutter med å definere et diskret system som kategorien av punkter i en liten kategori.

 

 

Uwe Wolter, UiB

Indexed vs. Fibred Structures – A Field Report

Sammendrag: Based on experiences in areas like Algebraic Specifications, Abstract Model Theory, Graph Transformations, Coalgebras and Foundation of Model Driven Software Engineering, I discuss the use of indexed and fibred structures in specification formalisms.

I consider their relationship as well as their advantages and disadvantages. Especially, I address the topics: model amalgamation, Grothendieck construction, van-Kampen square and (deep) meta-modeling.

 

Påmeldte

Petter Andreas Bergh, NTNY

Bjørn Ian Dundas, UiB

Gunnar Fløystad, UiB

Ine Gabrielsen, UiB

Fernando Abellan Garcia, NTNU

Håkon Robbestad Gylterud, UiB

Johanne Haugland, NTNU

James William Hobson, UiB

Lukas Reidar Bråthen Knudsen, UiB

Joachim Tilsted Kristensen, UiO

Astrid Sol Næss, UiB

Lars Salbu, UiB

Arvid Siqveland, UiSø-Norge

Håvard Utne Terland, NTNU

Jon Eivind Vatne, BI

Uwe Wolter, UiB

Jan Magnus Økland, BCEPS