Triangulated Categories

Spring 2010

Preliminary plan:
  • Introduce triangulated categories.
  • Discuss triangulated categories both from an algebraic and topological point of view.
  • Study recent work of amongst others Schwede and Rouquier.
Primary sources:
  • S.I. Gelfand & Yu. I. Manin: Methods of Homological Algebra
  • M. Hovey, J.H. Palmieri & N.P. Strickland: Axiomatic Stable Homotopy Theory
  • H. Margolis: Spectra and the Steenrod Algebra
  • P. May: The Axioms for Triangulated Categories
  • A. Neeman: Triangulated Categories
  • C. Weibel: An Introduction to Homological Algebra
When and where:
  • Friday 10.15 - 12.00, room 734, Sentralbygg 2.
List of seminars:
Date Speaker Title Abstract Notes
26th March Marius Thaule Introduction to stable homotopy theory In this very brief introduction to stable homotopy theory, I will focus on Freudenthals suspension theorem and spectra.
12th March Petter Andreas Bergh The centre of a triangulated category We will introduce the centre of a triangulated category and discuss some of its properties.
19th February Petter Andreas Bergh The dimension of a triangulated category We will introduce the dimension of a triangulated category, a relatively new concept (Rouquier, 2008).
5th February Hermund André Torkildsen Examples of triangulated categories 2 We continue from last time, and we construct the derived category.
29th January Hermund André Torkildsen Examples of triangulated categories 1 Derived categories of abelian categories are triangulated, and we will give an introduction to these.
22nd January Petter Andreas Bergh Introduction to triangulated categories We will continue from last time.
15th January Petter Andreas Bergh Introduction to triangulated categories In this first seminar lecture we will start with an introduction to triangulated categories, with the defining axioms.