Elements of Category Theory 1000-1M07ET
Most of the lecture will be an introduction to Category Theory, covering the following notions and theorems: categories, functors, natural transformations, equivalence of categories, representable functors, The Yoneda Lemma, limits, colimits, adjoint functors, GAFT, SAFT, cartesian closed categories, presheaf categories, monads, Eilenberg-Moore and Kleisli algebras, Beck's Theorem. The lecture will be illustrated by examples taken mostly from algebra, topology and logic.
In the remaining part of the lecture I intend to discuss Grothendieck toposes from various points of view: as generalized topological spaces, universes of 'sets', and geometric theories. The participants' interests may substantially influence the choice of the material covered in this part.
The course will end with a written exam.
Type of course
Course coordinators
Assessment criteria
The grading will be made on the basis of
1. Active participation in class
2. Written solutions of a set of problems
3. Oral exam
Bibliography
General introduction:
S. MacLane, Categories for the Working Mathematician,
M. Barr, Ch. Wells, Category Theory for Computing Science
Topos Theory:
I. Moerdijk, S. MacLane, Sheaves in Geometry and Logic
M. Barr, Ch. Wells, Toposes, Triples and Theories
Handbooks:
P. T. Johnstone, Sketches of an Elephant: A Topos Theory Compendium
F. Borceux, Handbook of Categorical Algebra
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: