The goal of this seminar is to introduce the theory of Infinity Categories.
Our main application will be a construction of the stable category of spectra and the smash product with the language of infinity categories.
Location: Room 622
Meeting Time: Mondays 5:30pm EST
Reference: Introduction to Infinity-Categories by Markus Land.
1. Introduction to Infinity Categories (1.1, 1.2)
Carlos Andrés Alvarado Álvarez 01/27/24
We will introduce simplicial sets, nerves of categories and more to build up to the definition of an infinity category.
2. Joins and Fibrations (1.3, 1.4)
John Smith
Abstract.
3. Categorical Properties (2.1, 2.2, 2.3)
John Smith
Abstract.
4. Localizations (2.4, 2.5)
John Smith
Abstract.
5. (Co)Cartesian Fibrations (3.1, 3.2)
John Smith
Abstract.
6. Straigthening-Unstraigthening (3.3)
John Smith
Abstract.
7. Yoneda Lemma (4.1, 4.2)
John Smith
Abstract.
8. (Co)Limits (4.3, 4.4)
John Smith
Abstract.
9. Adjoint Functors (5.1, 5.2)
John Smith
Abstract.
10. Presentable Infinity Categories
John Smith
Abstract.
11. Tensor Product
John Smith
Abstract.