Category Theory
80-413/713 - Fall 2012
Instructor: Spencer Breiner
Office: Doherty Hall 4301-A
Office Hours: M 12:00-1:30, F 1:00-3:00
E-mail: sbreiner[at]andrew.cmu.edu
Classroom: Wean Hall 5403
Course Expectations
 


Announcements
12/12 - Final posted. Read the instructions on the test paper. No collaboration! Good luck.
11/28 - Correction on HW9, 2(b)
11/27 - Correction on HW9, 1(b)-(d)
11/24 - Posted HW9. Due Dec. 3
11/10 - Posted HW8. Due Nov. 19 (or electronically Nov. 21)
11/06 - Correction to HW7, question 1(a)
10/30 - Posted HW7. Due Nov. 12
10/6 - Posted HW5. Due Oct. 17
10/2 - Another correction to HW4, problem 2.
10/1 - Correction to HW4, problem 2.
9/28 - Changed Wed. office hours to Friday.
9/22 - Posted HW4. Modified due dates for HW4 & HW5.
9/18 - Correction to HW3, problem 1.
9/15 - Posted HW3.
9/13 - Corrected another typo on HW2, question 4d. Added extra credit to question 4.
9/12 - Corrected typo on HW2, questions 4b & 4c.
9/08 - Office hours added. Second homework posted.
8/22 - The first day of class is Monday, August 27 at 10:30 AM in Wean 5403!


Homework SetDue Date

Homework 1 (LaTeX) Wednesday, Sept. 5
Homework 2 (LaTeX) Monday, Sept. 17
Homework 3 (LaTeX) Monday, Sept. 24
Homework 4 (LaTeX) Wednesday, Oct. 3
Midterm Wednesday, Oct. 10
Homework 5 (LaTeX) Monday, Oct. 22
Homework 6 (LaTeX) Wednesday, Oct. 31
Homework 7 (LaTeX) Monday, Nov. 12
Homework 8 (LaTeX) Monday, Nov. 19
(or electronically: Wed. Nov. 21)
Homework 9 (LaTeX) Monday, Dec. 3
Final Thursday, Dec. 13 @ 4:00 PM


Grading & Course Expectations
General Remarks 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.

Textbook Category Theory, Steve Awodey, 2nd edition, Oxford Logic Guides #52.

Additional Texts More advanced: Categories for the Working Mathematician, Saunders Mac Lane, Springer.

Less advanced: Conceptual Mathematics, F. William Lawvere & Stephen Schanuel, Cambridge Univ. Press.

Grading
Homework:60% = 6% x 10 problem sets
Midterm:15%
Final:25%

Homework 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.

Handwritten solutions will be (grudgingly) accepted, though typed answers are preferred. Messy or illegible answers will get one warning before losing credit.

Homework is due at the end of class on the due date indicated above. Late papers will receive the following credit:
     If < 48 hrs late:80%
If < 1 week late:50%
If > 1 week late:0%
E-mail submission (pdf only, NO MS WORD FILES) is acceptable as a date stamp, but you must also submit hard copies for grading.

Each student will get one free 48 hour late paper if I (Spencer) am notified by noon on the due date.

Midterm The midterm will be held in class on Wednesday, October 10th. Anyone in need of special arrangements or testing times must notify me by October 3rd, one week before the test.

Final Exam The format for the final (in-class vs. take-home) is still undecided. The final date & time (if needed) will be announced in a few weeks. I will update this space and inform the class on format by the 10th week of classes (Oct. 31st) at the latest.

80-413 vs.
80-713
As usual at Carnegie Mellon, the undergraduate and graduate sections of this course will be taught together. However, those students enrolled in the graduate section will be expected to work a little bit harder. Each homework set will contain 1-2 "starred" problems which only the 80-713 students will be expected to solve. The tests may also have additional "starred" problems.

Also, I am considering asking graduate students to write a short exposition of some aspect of category theory which is outside the scope of this class. I will discuss this in class, and provide more details by the 10th week of classes (Oct. 31st) at the latest.

Extra Credit I will offer students three (3) percentage points on their final grade if they typeset all of their assignments in LaTeX, a markup language designed for writing mathematical and scientific papers. To receive credit all of each assignment, including commutative diagrams, must be typeset.

In order to create documents using LaTeX, you will first need to install a LaTeX compiler. Here are instructions for installation on Windows, Mac or Linux (Ubuntu/Debian). I also recommend using a LaTeX editor like TeXmaker to help keep track of the LaTeX commands for various mathematical symbols. You will also need to some packages that supplement the basic LaTeX installation. These are probably included in your installation by default, but in case they aren't you can download them here: amssymb, amsmath and xypic.

Now you can create a document by feeding a .tex file into your compiler; you can probably do this from within your LaTeX editor. Please make sure your output is a PDF (rather than a PS or DVI). To get you started, you can look at the .tex files that I wrote for the homework sets.

In addition, I will post the LaTeX files that I write for the Homework sets, with some comments, to help get you started. You might also want to look at this collection of LaTeX examples (commented TeX input, PDF output). I will offer a session outside of classtime to help acquaint students with LaTeX. However, this will also require a good deal of self-guided learning on the student's part. Fortunately, there are many good resources available on the internet. In particular, I recommend the guide at WikiBooks.