Introduction to Topos Theory

Topos theory is a branch of mathematics, based on category theory, which has connections to both algebraic geometry and mathematical logic. Within mathematical logic it can be used to give alternative, more flexible foundations for all of mathematics, and in particular provides the foundation for subjects such as synthetic differential geometry. More recently, the work of Olivia Caramello has shown that toposes can be used to provide bridges between distinct mathematical areas. The aim of this class is to provide an introduction to topos theory for those who have some elementary understanding of category theory and mathematical logic, with a goal of proceeding far enough (either this term or in the spring) to understand Caramello's programme.

Abstract：

We will introduce Grothendieck toposes and show how some portions of the first-order categorical logic we have been discussing can be interpreted inside them.

One resource we are following is

https://www.oliviacaramello.com/Unification/ToposTheoreticPreliminariesOliviaCaramello.pdf.