Mathematics 617: Category Theory

Instructor: Jonathan Smith, 496 Carver, 4-8172 (voice mail)

e-mail: jdhsmithATiastateDOTedu (substitute punctuation)

Office Hours: Mon. 10am, 3:10 pm; Wed. 10am; Fri. 10am (subject to change)

Grading: based on five graded homework assignments (last due Wed., 12/9).

Click here for information about special accommodations.

Textbook: S. Mac Lane, Categories for the Working Mathematician, 2nd. ed., Springer, ISBN 0-387-98403-8

The book by Adámek-Herrlich-Strecker is also available online (4MB).

Study Plan: reserve 1 - 2 hours for homework between each pair of classes. Successful performance in the class depends critically on completion of the homework assignments.

Communication devices must remain switched off during the class periods.

Additional Mathematics course policies

Syllabus: Basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, cartesian-closed and enriched categories.


12/9 for 12/11: Read Mac Lane, Sections VII.2 - 3.

Take-home final due 12/9

12/7 for 12/9: Read Mac Lane, Section VII.1.

12/4 for 12/7: Read Mac Lane, Sections VIII.2 - 3.

12/2 for 12/4: Read Mac Lane, Sections I.8, VIII.1.

11/30 for 12/2: Read Mac Lane, Section IV.5. Do IV.5 Exercise 1.

11/18 for 11/30: Read Mac Lane, Section V.1. Do V.1 Exercises 3, 4, 6.

Fourth graded homework due 11/18:
Three questions from the following list of five: Section III.6: 3, 4; Section IV.4: 1, 2, 3.

11/16 for 11/18: Read Mac Lane, Section V.5. Do V.5 Exercise 1.

11/9 for 11/11: Complete reading of Mac Lane, Section IV.4.

11/6 for 11/9: Read Mac Lane, Section IV.3. Do IV.3 Exercise 4(a).

11/2 for 11/4: Read Mac Lane, Section III.2. Do III.2 Exercise 2.

10/21 for 10/23: Read Mac Lane, Section IV.4, through the proof of Theorem 1.

10/19 for 10/21: Read Mac Lane, Section IV.6. Do IV.6 Exercise 1.

Third graded homework due 10/26:
Three questions from the following list of five: Section IV.2: 4, 5, 9, 11, 12.

10/16 for 10/19: Read Mac Lane, Section IV.2.

10/12 for 10/14: Read Mac Lane, Section II.6, also first page and last four paragraphs of Section III.1.

10/9 for 10/12: Read Mac Lane, Section IV.1, first six pages. Do IV.1, Exercise 3.

10/5 for 10/9: Read Mac Lane, Section II.3. Do II.3 Exercises 1 - 3.

9/30 for 10/2: Read first half of Mac Lane, Section III.6.

Second graded homework due 10/5:
Three questions from the following list of five: Section III.4: 4, 5, 8, 10; Section III.5: 5.

9/28 for 9/30: Read Mac Lane, Section II.6 through "augmentation". Do II.6, Exercise 2.

9/25 for 9/28: Read Mac Lane, Sections III.3, III.5. Do III.5, Exercise 1.

9/21 for 9/23: Read Mac Lane, Section III.3, from Coproducts through Pushouts. Do Exercise 5.

9/18 for 9/21: Complete reading of Mac Lane, Section III.4. Do Exercise 9.

First graded homework due 9/18:
Three questions from the following list of five: Section I.4: 3, 5; Section II.4: 4, 6, 7.

9/14 for 9/16: Read Mac Lane, Section III.4, from Products through Pullbacks.

9/11 for 9/14: Read Mac Lane, Section II.4. Do Exercise 3.

9/4 for 9/9: Read Mac Lane, Sections II.1-2.
  1. Give an example of a monoid M that is not isomorphic to its opposite Mop.
  2. Prove that there is no monoid isomorphism between M and Mop.
9/2 for 9/4: Read Mac Lane, Section I.4.

Zero-th graded homework due 9/4:
Three questions from the following list of five: Section I.3: 2, 4; Section I.5: 6, 7 ("... every arrow in Set with non-empty domain is ..."), 9.

8/31 for 9/2: Read Mac Lane, Section I.3.

8/28 for 8/31: Read Mac Lane, Section I.5.
  1. Show that the inverse of an invertible morphism is unique.
  2. Give an example of a monomorphism in Set which is not split.

8/26 for 8/28: Read Mac Lane, Sections I.1, I.2.
  1. Consider the function sending each object of a category to the identity function at that object. Show that the function is injective.
  2. Show that the identity morphism at an object of a category is uniquely determined by Mac Lane's condition (2) on page 8.

8/24 for 8/26: Give an example of a directed graph C that is not isomorphic to its dual Cop. Prove that there is no directed graph isomorphism between C and Cop.