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.
(Last update: 10/07/2024)
Lecture 1: Introduction Notes
Lecture 2: Model categories Notes
Lecture 3: Simplicial sets Notes
Lecture 4: Quasi-categories Notes
Lecture 5: Quasi-category of quasi-categories Notes
Lecture 6: Limits and colimits: definition Notes
Lecture 7: Limits and colimits: functoriality Notes
Lecture 8: Limits and colimits: model categories Notes
Lecture 9: Limits and colimits: Kan extensions Notes
Lecture 10: Limits and colimits: commutativity Notes
Lecture 11: Yoneda lemma Notes
Lecture 12: Adjoint functors Notes
Lecture 13: Presentable infinity categories Notes
Lecture 14: Spectra Notes
Lecture 15: Stable infinity categories Notes
Lecture 16: t-structures Notes
Lecture 17: Derived infinity categories Notes
Lecture 18: Dold--Kan correspondence Notes
Lecture 19: Cartesian fibrations Notes
Lecture 20: Straightening and unstraightening Notes
Lecture 21: Infinity operads Notes
Lecture 22: Algebras Notes
Lecture 23: Modules I Notes
Lecture 24: Modules II Notes
Lecture 25: Lurie tensor products and smash products Notes
Lecture 26: Tensor products of infinity operads Notes
Lecture 27: E_infty rings Notes
HTT = Higher Topos Theory
HA = Higher Algebra
SAG = Spectral Algebraic Geometry
Ker = Kerodon