## Mathematics 617: Category Theory

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

e-mail: jdhsmithATmathDOTiastateDOTedu (substitute punctuation)

Office Hours: Mon. 11am, 2:10 pm, 5:30pm; Wed. 11am, 2:10pm (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

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: Chapters I - IV

### Homework Assignments

Fifth graded homework due 12/6:
Three questions from Section 3.5: 2, 5;
Section 3.6: 3, 4; Section 11.3: 1.

Fourth graded homework due 11/13:
Three questions from Section 4.4: 1, 2, 3;
Section 4.5: 1, 2 (but not "Does this generalize ...").

Third graded homework due 10/27:
Three questions from Section 4.2: 4, 5, 9, 10, 12.

10/18 for 10/20: In the adjunction
A( FX , A ) = X( X , GA )
show that the counit is a natural transformation.

10/16 for 10/18: For the natural isomorphism
φX , A : A( FX , A ) = X( X , GA )
in an adjunction, show that
φX , A ( f ) = Gf o ηX

10/13 for 10/16: For the natural isomorphism
φX , A : A( FX , A ) = X( X , GA )
in an adjunction, specify domain and codomain functors for the natural transformation
φ- , A

10/11 for 10/13: Describe the counit of the adjunction
Mon( FL , M ) = Set( L , GM )
for a set L and a monoid M.

10/9 for 10/11: Describe the counit of the Currying adjunction.

Second graded homework due 10/4:
Three questions from Section 3.4: 4, 5, 8, 9, 10.

First graded homework due 9/18:
Three questions from Section 1.4: 1, 2, 3, 4, 6.

Zero-th graded homework due 9/1:
Three questions from Section 1.5: 2, 3, 4, 6, 7.

8/23 for 8/25: 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.