Introduction to Topos Theory 24

Info. Lectures of 90 minutes each. First semester of 2024. Meeting once a week. The lectures will be delivered at Humanisten every Monday from 10 to 12 o'clock.

Date	Room	Date	Room	Date	Room
01/04		10/04	J406	22/4	J442
08/04	J236	15/04	J236	29/4	J442

Syllabus. (1) Topoi as spaces. (2) Topoi as sets. (3) Topoi as objects. (4) Topoi as theories.

Description. The course is an introduction to Topos Theory. Topos theory emerged from the Gothendieck school of Algebraic Geometry in the 60s and since then has florished in many directions. In its original field it became the standard language and technology in which a variety of problems has been phrased and solved. Since the 70s a number of category theorists started looking at Topos Theory with motivations coming from logic, this tradition finds its seminal work in the PhD thesis of Monique Hakim. The course reflects this multifacets nature of topos theory and presents both its logical and geometric aspects, stressing on the relevance of their intertwining.

Exam rules. The PhD students that want to have credits for the course will have an oral interview.

Audience and Prerequisites. The course is designed for an audience of PhD students and researchers interested in the topic. A good knowledge of the language of category theory will be a prerequisite for the audience (the equivalent of the whole (!) book by Emily Riehl, Category theory in Context), or the local course in Category Theory offered at the Master in Logic.

The below offers an exercise sheet covering the whole content of the course. Use it help you to familiarise with the subject. Notice that the exercise sheets are not graded and completely optional, they are meant to offer a playground to familiarise with the topic.