For questions,
you can contact me by e-mail (vanderweide@inf.elte.hu) or ask me during one of the lectures.
The lectures are on Friday between 8:00 and 10:00,
and a detailed schedule can be found below.
Examination
This course will be examined with homework exercises
and a presentation.
There will be three sets of homework exercises
The first set covers the material of lectures 1 to 4.
It is available here,
and the deadline is 16 October.
You can hand it in via e-mai (vanderweide@inf.elte.hu)
or you can give it to me during the lectures.
The second set covers the material of lectures 5 to 7.
It will be published on 6 November,
and the deadline is 20 November.
The third set covers the material of lectures 8 to 10.
It will be published on 27 November,
and the deadline is 11 December.
Solutions to the homework exercises either be submitted in person or via e-mail.
In the final three weeks of the course,
there will be student presentations.
The final grade is the average of the grades of the homework assignments
and the final presentation.
A list of topics for the final presentation is available here.
If you would like to present another topic,
please contact me via e-mail.
The final grade is determined from the average of each grade item using the following scheme.
1: <55%
2: ≥55%, <65%
3: ≥65%, <75%
4: ≥75%, <85%
5: ≥85%
Course Material
The lecture notes are under development
and will be updated regularly.
The current version is available here.
Presentations
Topic 1: Elementary toposes
Topic 2: Categories with Families taken
Topic 3: 2-categories
Topic 4: symmetric monoidal closed categories
Course Schedule
Lecture 1 (11 September 2026):
definition of categories, examples of categories, monomorphisms/epimorphisms/isomorphisms.
We discussed Section 1.1.
Recommended exercises: 1.1 to 1.8
Lecture 2 (18 September 2026):
basic limits and colimits.
We discussed Sections 1.2 and 2.1
Recommended exercises: 1.9 to 1.16, 2.1, 2.2, 2.8, 2.9, 2.12, 2.13
Lecture 3 (25 September 2026):
functors and natural transformations
We discussed Sections 2.2 and 3.1 (Section 2.3 is optional)
Recommended exercises: 2.3 to 2.7, 2.10, 2.11, 3.1 to 3.4
Lecture 4 (2 October 2026):
algebras and coalgebras
We discussed Sections 3.2 and 4.1 (Section 3.3 is optional)
Recommended exercises: 3.5 to 3.9, 4.1, 4.4, 4.5, 4.8, 4.9
Lecture 5 (9 October 2026):
Q&A session for first homework sheet
Lecture 6 (16 October 2026):
adjunctions
We disscussed Section 5.1 (Sections 5.2 and 5.3 optional)
Recommended exercisess: 5.1-5.4, 5.7
No lecture on 23 October 2026 (public holiday) and on 30 October 2026 (autumn break)
Lecture 7 (6 November 2026):
monads, the Yoneda lemma
Lecture 8 (13 November 2026):
Q&A session for second homework sheet
Lecture 9 (20 November 2026):
hyperdoctrines and first-order logic (part 1)
Lecture 10 (27 November 2026):
hyperdoctrines and first-order logic (part 2)
Lecture 11 (4 December 2026):
student presentations
Lecture 12 (11 December 2026):
student presentations