Reading/video assignments, notes and Zoom recordings in chronological order

Readings written in black are from Equivariant stable homotopy theory and the Kervaire invariant problem by Mike Hill, Mike Hopkins and myself, 2021.

Readings written in green are from Category Theory in Context by Emily Riehl, 2017.

Numbered chalk board videos (each under 10 minutes) are from The Catsters’ Category Theory Videos, mostly by Eugenia Cheng, with a few by Anatoly Kamchatnov, made in 2007.

Handwritten lecture notes and links to Zoom recordings will be posted soon after each lecture.

• February 1, 2021. Categories and functors. Read 2.1B and 2.1C and/or pages 1-8 and 13-22. Eugenia Cheng with Stephen Colbert Lecture notes Zoom video Zoom audio

• February 3, 2021. Sets, groupoids and topological spaces. Read 2.1D and 2.1E. Lecture notes Zoom video Zoom audio

• February 8, 2021. Natural transformations and equivalences, and functorial factorizations. Read 2.2A and 2.2B and/or pages 23-35. See videos 18 and 19. Lecture notes The recording was interrupted by a computer crash a few minutes in, and is therefore divided into two parts. Zoom video part A Zoom video part B Zoom audio part A Zoom audio part B

• February 10, 2021. The Yoneda lemma and introduction to adjoint functors. Read 2.2C and/or Chapter 2. See videos 20, 21 and 22. Lecture notes This recording was also interrupted by a computer crash a few minutes before the end, and is therefore divided into two parts. Zoom video part A Zoom video part B Zoom audio part A Zoom audio part B

• February 15, 2021. Imatatation Game trailer. Alan Turing page. More about the Yoneda lemma. Lecture notes Zoom video Zoom audio

• February 17, 2021. Adjoint functors. Read 2.2D and/or pages 115-125. See videos 23-29 for the general theory and videos 30-34 (by Anatoly) for some interesting examples. Pullbacks and oushouts, limits and colimits. Read 2.3A and 2.3B and/or pages 73-88. Lecture notes Zoom video Zoom audio

• February 22, 2021. A Beautiful Mind. More about limits and colimits. Read 2.3C and/or pages 90-105. Lecture notes Zoom video Zoom audio

• February 24, 2021. Kan extensions. Read 2.5 and/or Chapter 6. Lecture notes Zoom video Zoom audio

• March 1 and March 3. No classes.

• March 8, 2021. Ends and coends. Read 2.4. Lecture notes Zoom video Zoom audio

• March 10, 2021. Lecture by Wesley Smith on Haskell. Slides Zoom video Zoom audio

• March 15, 2021. Symmetric monoidal categories. Read 2.6 and/or E.2. Lecture notes Zoom video Zoom audio

• March 17, 2021. More symmetric monoidal categories and enriched categories. Read 3.1. Lecture notes Zoom video Zoom audio

• March 22, 2021. Lecture by Yuxin Luo on simplicial sets. Read 3.5. Zoom video Zoom audio

• March 24, 2021. The Day convolution. Read 3.3. Slides Zoom video Zoom audio

• March 29, 2021. Lecture by Charlotte Aten on algebraic theories and monads. Read 2.2E and/or Chapter 5. Slides Zoom video Zoom audio YouTube video

• March 31, 2021. Lecture by Vaibhav Sutrave on model categories. Read 4.1 and 4.2. Also see a series of 5 lectures by Scott Balchin. Notes. Zoom video Zoom audio

• April 5, 2021. Toward infinity categories. Read 1.1 of Riehl-Verity. Lecture notes Zoom video Zoom audio

• April 7, 2021. The definition of a quasi-category. Read 1.1 of Riehl-Verity. Lecture notes Zoom video Zoom audio

• April 12, 2021. More about quasi-categories. Contractbility of the space of compistierts of a pair of composable morphisms. Read sections 1 and 2 of Groth. Lecture notes Zoom video Zoom audio

• April 14, 2021. More about quasi-categories. Higher morphisms, limits and colimits. Read sections 1 and 2 of Groth. Lecture notes Zoom video Zoom audio

• April 19, 2021. Lecture by Vanessa Matus de la Parra on Dynamical systems and category theory. Lecture notes Zoom video

• April 21, 2021. Lecture by Jorge Olivar on Dynamical systems and category theory.Zoom video Zoom audio

• April 26, 2021. Lecture by Chuanyi Wang on Quantum mechanics and category theory. Reference: Kindergarten Quantum Mechanics and Introducing categories to the practicing physicist, both by Bob Coecke. Zoom video Zoom audio

• April 28, 2021. Lecture by Linus Ge on Monads. Read 5.1 and 5.2. No recording available, sorry.

• May 3, 2021. Lecture by Zheng Zhu on Categories on algebraic gebporetyr, especially sheaf theory. Zoom video Zoom audio

• May 5, 2021. Lecture by Samuel Restoy on Categories on algebraic K-theory on Sheaves. Zoom video Zoom audio