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.

Prerequisites
The course Category Theory, as given in Mastermath or equivalent.

Aim of the course
Familiarize the students with topos-theoretic techniques, especially in Logic.

• Elementary toposes
• Geometric morphisms
• Inclusions and surjections
• Classifying toposes
• Logical aspects of toposes
• Example of a non-Grothendieck topos

Lecturers
Jaap van Oosten (UU)