# **Category Theory**

### LMU Munich

### SommerSemester 2011

### **Course Information**

Place: Theresienstr. 39 B004

Time: Mo 4 - 6

Instructor: Steve Awodey

Office: Theresienstr. 39, B421 (Math); Ludwigstr. 31, 123 (MCMP)

Office Hour: Monday 2-3 (Math); Thursday 4-5 (MCMP), or by appointment.

Phone: x4418

Email: awodey@cmu.edu

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.

### **Prerequisites**

Some familiarity with abstract algebra or logic.
### **Texts**

Course notes will be provided.

Also recommended are the following:
- Awodey: Category Theory.

- Barr & Wells: Categories for Computing Science (3rd edition).

- Borceux: Handbook of Categorical Algebra.

- Mac Lane: Categories for the Working Mathematician. (the standard reference)

**Topics to be covered**

- Categories
- Functors
- Natural transformations
- Functor categories
- Yoneda's lemma
- Limits
- Universality
- Adjointness
- Cartesian closed categories
- Categorical logic

### **Lecture Notes**

Weekly lecture notes are here.
### **Homework**

Weekly problem sets are here.

Steve Awodey

awodey@cmu.edu