Olivia Caramello's website



Topos theory course at Insubria

I have recently taught (in English) a Master-level course on Topos Theory at the University of Insubria (Como, Italy). The lectures started on the 2nd of October 2018 and finished on the 18th of December.

Slides used as a support for my lectures:

Lecture 1 - Overview of the course
Lectures 2-3-4 - Categorical preliminaries
Lectures 5-6 - Sheaves on a topological space
Lectures 7-14 - Sheaves on a site; basic properties of Grothendieck toposes; local operators
Lectures 15-18 - Geometric morphisms; flat functors; morphisms between sites.
Lectures 19-20 - The interpretation of logic in cateogories
Lectures 21-22 - Classifying toposes and the 'bridge' technique

Students from Insubria can access the videos of the lectures at this link by inserting their credentials.

The exercises for the exam are available here.

More information about the course is available at the course webpage ; see also these presentation slides.

Teaching experience

Introductory text

Click here for a(n unpolished) draft of the first two chapters of my book "Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges'" (Oxford University Press, 2017). This 64 pages text is a self-contained introduction to toposes, categorical logic and the 'bridge' technique requiring only a basic familiarity with category theory.

Research-level lecture courses