Prerequisites
There are no particular prerequisites for this course.
Aims of the course
Most mathematicians are defined by the kind of mathematical structure they study; category theorists are defined by the way they approach mathematical structure.
The guiding idea of category theory is that no mathematical structure exists on its own; it is always an individual in a broader mathematical community. The other members of this community share the same structure, and the individual is connected to them by various structure-preserving maps. In category theory one only considers those properties that can be formulated purely in terms of how individuals relate to other individuals via structure-preserving maps, thus abstracting away from any unique individual characteristics which cannot be formulated in these terms. Contrary to what one might expect, it turns out that many interesting properties can be captured this way.
Indeed, the language of category theory is both rich and useful and by now pervades modern mathematics (in particular, algebra, algebraic geometry and topology), mainly due to the influence of mathematicians like Grothendieck and MacLane.
The aim of this course is to introduce the students to the language of category theory, its main concepts (such as limits and colimits, adjoint functors, monads, presheaves and the Yoneda Lemma).
Homework/exam
The course will be concluded by a written exam, for which you must obtain at least the grade 5. There are, during the course, hand-in exercises, which count for 30% of your final grade. That is, your final grade will be calculated as follows: let H be your average grade for the hand-in exercises and W your grade for the written exam. Provided W is at least 5, your final grade will be (3H + 7W)/10. (This applies to the retake exam as well.)The course will be concluded by a written exam, for which you must obtain at least the grade 5. There are, during the course, hand-in exercises, which count for 30% of your final grade. That is, your final grade will be calculated as follows: let H be your average grade for the hand-in exercises and W your grade for the written exam. Provided W is at least 5, your final grade will be (3H + 7W)/10. (This applies to the retake exam as well.)
Lecture Notes/Literature
Recommended literature:
Tom Leinster, Basic category theory, Cambridge University Press, 2014.
https://arxiv.org/abs/1612.09375
Emily Riehl, Category theory in context, Dover publications, 2016.
http://www.math.jhu.edu/~eriehl/context.pdf
Students how are interested in foundational questions can have a look here:
https://arxiv.org/pdf/0810.1279.pdf
- Docent: Benno van den Berg