Saunders Mac Lane

Category Theory

80-413/713 — Spring 2015

Meeting place and time: Wean Hall 8427 — MW 1:30–2:50pm
Instructor: Ulrik Buchholtz (ulrikb[at]
Office: Baker Hall 152
Office Hours: Tuesdays 3:15–5:00pm, or by appointment
TA: Egbert Rijke (erijke[at]
Office: Doherty Hall 4302A
Office Hours: Mondays 3:00–4:00pm

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 (ahem, discourse). 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 shall follow the book quite closely, taking about one week for each chapter.

Additional Texts & Resources



Homework sets will typically consist of 4-6 problems, available from the links above. 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.

Extra credit

We will give students 3 percentage points on the total score for the course if they typeset all of their assignments in LaTeX. To receive credit, all of each assignment, including commutative diagrams, must be typeset.


The midterm will be held in class on Wednesday, February 25. Anyone in need of special arrangements or testing times must notify me by February 18, one week before the test.


The final will be a 24 hour take-home exam: From Wednesday, May 6, 4pm, until Thursday, May 7, 4pm.

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.

See the announcements for Egbert's LaTeX tutorial and the source code for the homework sets.