Mathematics 617: Category TheoryInstructor: 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 AssignmentsFifth 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 φ_{X , A} : A( FX , A ) = X( X , GA )in an adjunction, show that φ_{X , A} ( f ) = Gf o η_{X} 10/13 for 10/16: For the natural isomorphism φ_{X , 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 C^{op}. Prove that there is no directed graph isomorphism between C and C^{op}. |