Projects in Previous Years

2nd Semester 2011/12: Category Theory

Teaching assistant: Sumit Sourabh
If you are interested in this project, please contact Kohei and Sumit by email.
This project will introduce students to category theory, a branch of abstract algebra that has found many applications in mathematics, logic, and computer science, among others. Category theory provides a framework of formal methods that enable structural and unificatory approaches to phenomena that occur commonly across different subjects. The goal of this project is to acquaint students with these methods and to prepare them to apply category theory to many topics in logic, computer science and other fields, such as duality theory, coalgebraic logic, and categorical logic.

The first three weeks of the course will consist of introductory lectures by the instructor and exercise/discussion sessions, and will cover fundamental concepts and methods in category theory such as the Yoneda lemma, adjoints, and monads. In the final week, students will present materials on applied topics.

First-order logic (and familiarity with basic notions in set theory). Familiarity with basic algebras such as monoids, groups, partial orders and lattices will be helpful.
Students will work on exercise problems and submit homework every week. In the final week, they will give presentations on topics in logic, computer science, or other areas that use category theory. Participation in class discussions will also be assessed.
Course webpage: Follow this link.