The course Category Theory, as given in Mastermath.
Aim of the course
Toposes were defined by Grothendieck and his co-workers, as a generalization of categories of sheaves on topological spaces: a "Grothendieck topos" is the category of sheaves on a site, where a site is a category with a suitably defined "Grothendieck topology".
In the 1960's, Lawvere formulated the notion of an "elementary topos": a type of category characterized in purely categorical terms.
It turns out that toposes have an "internal logic", and they are useful both in geometry and logic. In the course, we shall treat the following topics: elementary toposes, geometric morphisms, inclusions and surjections, classifying toposes, logical aspects of toposes, and an example of a non-Grothendieck topos.
The aim is to familiarize students with these topics and topos-theoretic techniques, especially in Logic.
Jaap van Oosten (UU)
- Docent: Jaap van Oosten