Mathematics 584: Category TheoryInstructor: Jonathan Smith, 496 Carver, 4-8172 (voice mail) e-mail: jdhsmithATmathDOTiastateDOTedu (substitute punctuation) Office Hours: Mon. 2:10 pm, 5:30pm; Wed. 2:10pm, 4:10pm, 5pm (subject to change)
Grading: based on five graded homework assignments.
Textbook: S. Mac Lane, Categories for the Working Mathematician, 2nd. ed., Springer, ISBN 0-387-98403-8 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: Chapters I - IV Homework AssignmentsFifth graded homework due 12/8:Three questions from the following:
Fourth graded homework due 11/10: Three questions from Section 4.2: 5, 9, 10, 12; Section 4.5: 3. 10/27 for 11/1: Given an adjunction ( F : X --> A , G : A --> X , h , e ) ,prove that e_{Fx} o Fh_{x} = id_{Fx} for each object x of X . 10/25 for 10/27: Section 4.2: 4. 10/18 for 10/22: Section 5.1: 6, 7. Third graded homework due 10/18: Three questions from Section 2.4: 6; Section 3.4: 5, 6, 8; Section 3.6: 1. 10/1 for 10/4: Section 2.4: 2, 4. 9/27 for 10/1: Section 3.6: 4. 9/22 for 9/27: Sections 2.3: 1, 2; 3.5: 1. Second graded homework due 9/22: Three questions from Section 1.5: 1, 4, 5, 6, 7. 9/13 for 9/15: Section 1.4: 2, 3. 9/8 for 9/13: Section 1.5: 8. Also: Let T_{1} and T_{2} both be terminal objects of a given category C. Prove that T_{1} and T_{2} are isomorphic. First graded homework due 9/8: Three questions from the two assignments below (Sections 1.3, 1.4). 8/30 for 9/8: Section 1.4: 1, 2, 3. 8/27 for 9/8: Section 1.3: 2, 3(a)(b), 4. 8/25 for 8/27: Let ≤ be a pre-order on a set S. Define a relation E on S by x E y if and only if x≤y and y≤x.Show that E is an equivalence relation on S. 8/23 for 8/27: Show that id : Ob(C) --> Mor(C) is 1-1. |