Meeting place and time: Wean Hall 8427 — MW 1:30–2:50pm

Instructor: Ulrik Buchholtz (ulrikb[at]andrew.cmu.edu)

Office: Baker Hall 152

Office Hours: Tuesdays 3:15–5:00pm, or by appointment

TA: Egbert Rijke (erijke[at]andrew.cmu.edu)

Office: Doherty Hall 4302A

Office Hours: Mondays 3:00–4:00pm

- Actually, the final exam shall be given for any 24-hour period
*of the student's choosing*(by university policy). So let me know before*Friday May 1*when you want to take the final! - Some references regarding the final two weeks' discussion on monoidal categories.
- Homework #12 is due Wednesday, April 22, at 1:30pm: PDF, LaTeX, LaTeX preamble
- Homework #11 is due Wednesday, April 15, at 1:30pm: PDF, LaTeX, LaTeX preamble
*Tuesday, April 7, 4pm*: for HW #10, problem 3, you do not need to check naturality of the adjunctions.- The final exam will be released on Wednesday, May 6, at 4pm, and will be due 24 hours later, on Thursday, May 7, at 4pm.
- Homework #10 is due Wednesday, April 8, at 1:30pm: PDF, LaTeX, LaTeX preamble
- Homework #9 is due Wednesday, April 1, at 1:30pm: PDF, LaTeX, LaTeX preamble
- Homework #8 is due Wednesday, March 25, at 1:30pm: PDF, LaTeX, LaTeX preamble
- Homework #7 is due Wednesday, March 18, at 1:30pm: PDF, LaTeX, LaTeX preamble
- Homework #6 is due Wednesday, March 4, at 1:30pm: PDF, LaTeX, LaTeX preamble
*Wednesday, February 18, 9:30am:*Updated HW5, problem 4(b), to specializeto the category of sets. The problem is not solvable for arbitrary categories.C *Monday, February 16, 3:10pm:*Updated HW5, problem 1, to add that the category has all pullbacks.- Homework #5 is due Wednesday, Febrary 18, at 1:30pm: PDF, LaTeX, LaTeX preamble
- Homework #4 is due Wednesday, Febrary 11, at 1:30pm: PDF, LaTeX, LaTeX preamble
- Homework #3 is due Wednesday, Febrary 4, at 1:30pm: PDF, LaTeX, LaTeX preamble
- NB: Office hours will from now on be on Tuesdays 3:15–5:00pm, or by appointment.
- NB: Office hours Tuesday, January 27, are
*moved*to 3:15–5:00pm. - NB: Office hours Thursday, January 22, are
*cancelled*. - Homework #2 is due Wednesday, January 28, at 1:30pm: PDF, LaTeX, LaTeX preamble
*Wednesday, January 14, 4:40pm:*Updated HW1 with a replacement problem 5 that does not refer to free categories. We shall cover free categories in class on Monday, January 19.- Homework #1 is due Wednesday, January 21, at 1:30pm: PDF, LaTeX, LaTeX preamble
- Egbert has made a LaTeX how-to for the course: PDF, LaTeX, preamble
- The first day of class is Monday, January 12!

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*, 2^{nd} edition,
Oxford University Press, 2010.

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

- Saunders Mac Lane,
*Categories for the Working Mathematician*, 2^{nd}edition, Springer, 1998. - F. William Lawvere and Stephen Schanuel,
*Conceptual Mathematics: a first introduction to categories*, 2^{nd}edition, Cambridge University Press, 2009. - Tom Leinster,
*Basic Category Theory*, Cambridge University Press, 2014. - David Spivak,
*Category Theory for the Sciences*, The MIT Press, 2014. - The
*n*Lab: a wiki-lab on Mathematics, Physics and Philosophy from the point of view of (higher) category theory. They have pages on most concepts in our course and many beyond. - Category Theory: the entry at the Stanford Encyclopedia of Philosophy by Jean-Pierre Marquis discusses the history and philosophical significance of Category Theory.

- Homework: 60% = 7.5% times the sum of the best 8 homework scores (out of 12 sets)
- Midterm: 15%
- Final: 25%

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.

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.

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.