Topos Theory Seminar
Fall 2003

Organizers: Lars Birkedal, birkedal@itu.dk, Room 2.21, 3816 8868
Carsten Butz, butz@itu.dk, Room 1.17, 3816 8820

This is a Ph.D. seminar in which we study aspects of topos theory relevant to computer science. After having read material from Peter Johnstone's opus: Sketches of an Elephant: A Topos Theory Compendium we plan to pause and read parts of

Additional material can be found in Jaap van Oosten's notes on Basic Category Theory. Focus will be on Lambek/Scott.

To gain credit for this 7.5 ECTS seminar you have to participate actively in the discussions. Moreover, you have to take responsibility for at least one topic, stretching usually over more than a week.

Meeting time: We meet on Fridays, 14:00--15:30, Room 2.55.

Participants:

(birkedal@itu.dk, butz@itu.dk, volodya@itu.dk, hilde@itu.dk, mogel@itu.dk, noah@itu.dk, nina@itu.dk, m98rlp@math.ku.dk, bodil@math.ku.dk, m98mb@math.ku.dk)

Schedule:

Date Speaker Reading
Fri Aug 29  CB Introduction
Fri Sep 5  - No meeting
Fri Sep 12   A: NTS I.1 - I.6: Propositional calculus, deductive systems, cartesian closed categories
Fri Sep 19   A: NTS Continued
Fri Sep 26   B: CB I.8 - I.11: CCCs with coproducts, typed lambda calculus, relation between the two
Fri Oct 3   B: CB Continued
Fri Oct 10   C: CB II.1, II.2: Type theories
Fri Oct 17  - No meeting
Fri Oct 24   D: RM II.3, II.4: Internal logic of a topos, Peano's axioms
Fri Oct 31   D: RM II.5, II.6: The internal logic at work
Fri Nov 7   E: MB II.7: Choice, Boolean toposes (plus suplemental material)
Fri Nov 14   F: BB II.8, II.9: Topos semantics
Fri Nov 21   F: BB Continued
Fri Nov 28   H: RLP II.11 - II.14: Toposes and type theories (selection)
Fri Dec 5   G: MB II.10: Sheaves
Fri Dec 12   I: VS II.18: Sheaf representation
Fri Dec 19   J: RLP II.20, II.21: Intuitionistic principles