Triangulated categories were defined independently and around the same time by Puppe and Jean-Louis Verdier (1963). Verdier’s original work was in his PhD thesis based on the ideas of Grothendieck.

Triangulated Categories has applications in Algebraic Geometry, Representation Theory,Commutative Algebra, Algebraic Topology, Dynamical Systems and so on.

This note is prepared for a seminar on introduction to Triangulated Categories based on Neeman’s book.

triangulated category .pdf  ( almost 0.4 M.Byte)

triangulated category.pptx ( almost 1.9 M.Byte)

you can see  some important references of triangulated category below :

  1. A. Neeman, Triangulated categories, Annals of Mathematics Studies 148, Princeton University Press (2001).
  2. Daniel Murfet, Triangulated Categories ( Part I ),2007.
  3. Peter J. Freyd, Abelian Categories: an Introduction to the Theory of Functors, Harper & Row (1964).
  4. Marino Gran, Notes on regular, exact and additive categories, Summer School on Category Theory and Algebraic Topology, EcolePolytechniqueFederale de Lausanne, 11-13 September 2014
  5. JirıAdamek, Horst Herrlich, George E. Strecker, Abstract and Concrete Categories, The Joy of Cats
  6. S. MacLane, Categories for the Working Mathematician, Graduate texts in Mathematics 5,Springer, 1971.
  7. Jon Woolf, An introduction to derived and triangulated categories, PSSL, Glasgow, 2006.
  8. Sebastian Arne Klein, Reconstructive Geometry in certain Triangulated Categories, Utrecht University Department of Mathematics Master’s Thesis, under Supervision of Prof. G. Cornelissen,2010.