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.
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
