Abstract: The goal of the lectures is to give an overview of categorical logic in toposes and to justify the adage that a topos can serve as a universe for developing mathematics by developing algebraic geometry over a base topos.

 

1. Foundations of categorical logic

 

Elementary and Grothendieck toposes. Categorical logic, syntax and semantics, geometric logic.  

 

2. Relative algebraic geometry. 

 

Classifying toposes. Hakim-Cole spectra. Zariski and etale spectra of a ringed topos. Cohomology and the fundamental groupoids.

 

Predavanja će trajati otprilike 60 minuta (svako) i mogu se pratiti online putem sljedeće poveznice: