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.

1. Why stacks?
2. Categories
3. Equivalence of Categories and (co)limits
4. More (co)limits
5. Even more (co)limits
6. The functor of points
7. The Yoneda embedding part II
8. Grothendieck toplogies
9. Sites and Topoi
10. The canonical topology
11. Functoriality
12. Étaleness
13. More adjectives
14. Even more adjectives
15. Flatness and algebraic spaces
16. Algebraic spaces and equivalence realtions
17. Equivalence relations and group actions
18. Descent
19. More descent
20. 2-categories
21. Fibered categories
22. Stacks
23. Algebraic stacks
24. Stackification and quotient stacks