# 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
- Representations of categories , Part 1, 28/2/2007 (BR)
- 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

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

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

Oliver Kullmann
Last modified: Mon Apr 23 18:49:44 BST 2007