Theoretical Computer Science PhD Seminar (Hauptseminar)

Messages

• Next talk 25/4/2007 (15:00, Board room).

2006/07

• The subject for 2006/07 is categories for computer science .
• At the preliminary discussion (18/10/2006) a handout was distributed with the literature and the (preliminary) seminar schedule.

Talks

• Part I
  • Talk 1, OK, 25/10/2006 (RR) + 1/11/2006 (RR): Foundations of category theory (as handout; here are the slides )

  • Talk 2, Ken Johnson, 8/11/2006 (RR) + 15/11/2006 (RR)

  • Talk 3, Ulrich Berger, 22/22/2006 (RR) + 29/11/2006 (RR)

  • Talk 4, Matthew Lewsey, 6/12/2006 (Faraday E) + 13/12/2006 (RR)
• Part II
  • Talk 5, Temeshgen Kahsia, 14/2/2007 (BR) + 21/2/2007 (BR)
  • Talk 6, OK
    1. Representations of categories , Part 1, 28/2/2007 (BR)
    2. The adjoint functor theorem , Part 2, 14/3/2007 (BR)
  • Talk 7, Gift Samual, 21/3/2007 (BR) + 25/4/2007 (BR)
  • Talk 8, Liam O'Reilly
  • Further talks to be decided.

Exercises

1. For talk 1 here is the list of alluded exercises (referring to the handout version):
   1. page 7: show the three basic properties
   2. page 11: show the two main properties
   3. page 21: show that cat(G) is a category
   4. page 29: show that cat(X) is a category and that qos(C) is a quasi-ordered set
   5. page 33: show the two basic properties
   6. page 35: show the two basic properties
   7. page 36: show that cat(f) is a functor
   8. page 38: show the two statements
   9. page 40: show the two statements
   10. page 52: show that we have a meta-category
   11. page 53: show that the 16 categories are actually categories
   12. page 59: check that the three cat-functors are functors, and that dgg and qos are also functors
   13. page 64: show that the product category is actually a category
   14. page 65: show that the two V-functors (in the first two displayed equations) are functors, and show the (displayed) equation
   15. page 67: two free exercises
   16. page 68: show that the dual category is a category
   17. page 69: show that characterisation of the dual of categories of correspondences
   18. page 70: show the (displayed) equivalences
   19. page 71: fully specify the Hom-functor, and show that it is a functor
   20. page 73: show the assertion under point 2
   21. page 75: show that Fun(C, D) is a category
   22. page 76: "Exam"

2. For talk 2 : Special morphisms in categories: Cancellation and Inversion