## Mathematics 584: Category Theory

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

e-mail: jdhsmithATmathDOTiastateDOTedu (substitute punctuation)

Office Hours: Mon. 11am, 2:10 pm; Wed. 11am, 2:10pm, 5pm (subject to change)

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 Assignments

8/28 for 9/4: Show that  id : Ob(C) —Mor(C)  is 1-1.
8/30 for 9/4: 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.
9/6 for 9/13: Section 1.3: 2, 3(a)(b), 4, 5.
9/9 for 9/13: Section 1.4: 1, 2, 3.

Three questions from the above two assignments (Sections 1.3, 1.4).

9/23 for 9/27:
(a) Give an example of a poset with a bottom element, but no top element.
(b) Give an example of an infinite poset in which each subset has a bottom element, but no infinite subset has a top element. Prove that the example does have these properties.
9/25 for 9/27:
(c) Let T1 and T2 both be terminal objects of a given category C. Give a careful proof that T1 and T2 are isomorphic.
Also Section 1.5: 3.
9/27 for 9/30: Section 1.5: 2

Three questions from Section 1.5: 4, 5, 6, 7, 8.

10/11 for 10/14: Section 3.4: 1 (first part only, not Top), 6
10/16 for 10/18: Section 2.6: 2