Grothendieck topoi and Giraud’s theorem
The notion of a sheaf on a topological space can be generalised to a small category. To do so we must introduce additional structure since arbitrary categories lack a notion of coverings. This structure that we will define through the talk is called a Grothendieck topology. A Grothendieck topos is then defined as any category equivalent to the category of sheaves on a category endowed with a Grothendieck topology. We will state and give a sketch of the proof of Giraud’s theorem that gives sufficient and necessary conditions for a locally small category with all finite limits to be a Grothendieck topos. No prior knowledge of sheaf theory is needed to understand the talk.
Practical information
- Informed public
- Free
Organizer
- Bjørnar Hem
Contact
- Maroussia Schaffner