# Stacks Notes

Here are my handwritten notes for the Fall 2022 course on Stacks, taught by David Zureick-Brown. Of course, these notes are not a loyal representation of the course. The target audience was my 2022 self. Keep in mind that all the errors are mine and the merits should be credited to the lecturer. Use at your own risk; I took this notes as a stacks novice and my inexperience surely shows.

- Why stacks?
- Categories
- Equivalence of Categories and (co)limits
- More (co)limits
- Even more (co)limits
- The functor of points
- The Yoneda embedding part II
- Grothendieck toplogies
- Sites and Topoi
- The canonical topology
- Functoriality
- Étaleness
- More adjectives
- Even more adjectives
- Flatness and algebraic spaces
- Algebraic spaces and equivalence realtions
- Equivalence relations and group actions
- Descent
- More descent
- 2-categories
- Fibered categories
- Stacks
- Algebraic stacks
- Stackification and quotient stacks