Saunders Mac Lane

Category Theory

80-413/713 — Fall 2021

Time: Tuesdays and Thursdays 3:05PM–4:25PM
Room: TEP 1308

Instructor: Jonas Frey
Office Hour: Wednesdays 4:30–5:30 PM in Baker Hall BH148

TA: Fernando Larrain
Office Hour: Mondays 10:00–11:00 AM in Doherty Hall DH4302-A

Samuel Eilenberg


Course Description

Category theory is a formal discipline developed to study complex problems in algebra and geometry, and later applied in logic, physics, computer science and many other areas. As such, this course will be more like a math class than a typical philosophy section. In particular, students will be expected to provide formal arguments and proofs for homework and on tests.

At the same time, the course is relevant to a wide range of disciplines, so some students may be less conversant in mathematical jargon. For anyone that might be having trouble, here is a short how-to and here is a longer guide . Many more resources are easily available.


Steve Awodey, Category Theory, 2nd edition, Oxford University Press, 2010.

We will follow the book quite closely, taking about one week for each chapter.

Additional Texts & Resources



Homework sets will typically consist of 3-5 problems, and will be posted here each week. Solutions to all problems should be written out in full sentences and paragraphs. See here if you have questions about writing up solution sets. In your solutions, you may appeal to any fact which has been proved either in class or in the course textbook.

Homework is due at the beginning of class on the due date indicated on top. Late homework will not be accepted. E-mail submission (PDF files only) is preferred for LaTeX solutions, and counts as a timestamp. To account for illness or unforeseen personal circumstances, only the best 8 scores count toward the grade.

Homework has to be submitted via gradescope, by the time indicated on the homework sheet.


The final will take place on Friday December 10 from 5:30PM to 8:30PM.

80-413 vs. 80-713

The undergraduate and graduate sections of this course will be taught together. However, students enrolled in the graduate section will be expected to work a little bit harder. Each homework set will contain 1-2 starred problems that only the 80-713 students will be expected to solve. The tests may also have additional starred problems.


Students are encouraged to write their assignments in LaTeX. The Wikibook on LaTeX is a good place to start. We recommend using the tikz-cd package for creating commutative diagrams; see the manual for details. You will need an up-to-date installation of TeX Live to take advantage of the newest version of tikz-cd.