Fall 2024: Infinite Category Theory
We do not present results and even definitions in the logical order.
Some "exercises" in these notes are challenging and cannot be solved by methods introduced in the lectures, especially for those in the appendices.
Lecture 1: Introduction Notes (Last update: 10/07/2024)
Lecture 2: Model categories Notes (Last update: 10/07/2024)
Lecture 3: Simplicial sets Notes (Last update: 10/07/2024)
Lecture 4: Quasi-categories Notes (Last update: 10/07/2024)
Lecture 5: Quasi-category of quasi-categories Notes (Last update: 11/19/2024)
Lecture 6: Limits and colimits: definition Notes (Last update: 11/26/2024)
Lecture 7: Limits and colimits: functoriality Notes (Last update: 10/25/2024)
Lecture 8: Limits and colimits: model categories Notes (Last update: 10/18/2024)
Lecture 9: Limits and colimits: Kan extensions Notes (Last update: 11/29/2024)
Lecture 10: Limits and colimits: commutativity Notes (Last update: 11/29/2024)
Lecture 11: Yoneda lemma Notes (Last update: 11/29/2024)
Lecture 12: Adjoint functors Notes (Last update: 10/30/2024)
Lecture 13: Presentable infinity categories Notes (Last update: 11/12/2024)
Lecture 14: Spectra Notes (Last update: 11/20/2024)
Lecture 15: Stable infinity categories Notes (Last update: 11/20/2024)
Lecture 16: t-structures Notes (Last update: 11/21/2024)
Lecture 17: Derived infinity categories Notes (Last update: 11/20/2024)
Lecture 18: Dold--Kan correspondence Notes (Last update: 11/22/2024)
Lecture 19: Cartesian fibrations Notes (Last update: 11/26/2024)
Lecture 20: Straightening and unstraightening Notes (Last update: 11/29/2024)
Lecture 21: Infinity operads Notes (Last update: 12/16/2024)
Lecture 22: Algebras Notes (Last update: 12/10/2024)
Lecture 23: Modules I Notes (Last update: 12/10/2024)
Lecture 24: Modules II Notes (Last update: 12/16/2024)
HTT = Higher Topos Theory
HA = Higher Algebra
SAG = Spectral Algebraic Geometry
Ker = Kerodon