Category Theory
80-413/713
Spring 2006
Course Information
Place: BH 225B
Time: TR 3 - 4:20
Instructor: Steve Awodey
Office: Baker 152 (mail: Baker 135)
Office Hour: Monday 3 - 4, or by appointment
Phone: x8947
Email: awodey@andrew
Secretary: Baker 135
TA: Michael Warren
Office: Baker 135
Office Hour: Fridays 10:30 -- 11:20 in BH 150
Webpage: www.andrew.cmu.edu/course/80-413-713
Overview
Category theory, a branch of abstract algebra, has found many applications
in mathematics, logic, and computer science. Like such fields as elementary
logic and set theory, category theory provides a basic conceptual apparatus
and a collection of formal methods useful for addressing certain kinds of
commonly occurring formal and informal problems, particularly those involving
structural and functional considerations. This course is intended to acquaint
students with these methods, and also to encourage them to reflect on the
interrelations between category theory and the other basic formal disciplines.
To be followed by a Fall course on categorical logic.
Prerequisites
Some familiarity with abstract algebra or logic.
Texts
Course notes will be provided.
Also recommended, and on reserve in E&S Library, are the following:
- Barr & Wells: Categories for Computing Science (3rd edition).
- Borceux: Handbook of Categorical Algebra.
- Mac Lane: Categories for the Working Mathematician. (the standard
reference)
Requirements and Evaluation
Grades will be based on weekly homework and a final exam, according to the
scheme:
Homework: 75%
Final exam: 25%
Topics to be covered
- Elementary theory of categories
- Functors
- Natural transformations
- Functor categories
- Yoneda's lemma
- Limits
- Universality
- Adjointness
- Cartesian closed categories
- Monads and their algebras
- Categorical logic
Lecture Notes
Weekly lecture notes are here.
Homework
Weekly problem sets are here.
Steve Awodey
awodey@cmu.edu