Mathematics 617: Category TheoryInstructor: 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).
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.
Syllabus: Basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, cartesian-closed and enriched categories. Assignments12/9 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.
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.
8/26 for 8/28: Read Mac Lane, Sections I.1, I.2.
8/24 for 8/26: Give an example of a directed graph C that is not isomorphic to its dual C^{op}. Prove that there is no directed graph isomorphism between C and C^{op}. |