Rudiments of Category Theory Project

Welcome to the web page for the January project Rudiments of Category Theory. Here you will find information about the development of the course. In particular, you will find homework assignments and information about time and location. The person in charge of the project is Raul Andres Leal

The project will run from the 5th of January until the 30th of January.

In principle, there will be meetings three times per week. These meetings will be, in general, on Monday (P0.17 15-17), Wednesday (P0.16 15-17), and Friday (P0.16 15-17).

• Monday, January 5th, (P0.17 15-17) Introduction, Points, Natural Numbers and Diagonal Arguments.
• Wednesday, January 7th (P0.16 15-17) Categories and Functors.
• Friday, January 9th (P0.16 15-17) Natural transformations I, Diagrams and Universality.
• Monday, January 12th (P0.17 15-17) Natural transformations II.
• Wednesday, January 14th (P0.16 15-17) Limits, Colimits and Duality.
• Friday, January 16th (P0.16 15-17) Limits and Colimits II.
• Monday, January 19th (P0.17 15-17) Free time!!!!
• Wednesday, January 21th (P0.15b 11-13) Adjunctions I.
• Friday, January 23th (P0.16 15-17) Adjunctions II.
• Monday, January 26th (P0.17 11-13) Adjoint Functor Theorem.
• Thursday, January 29th (P0.16 11-13) Lawvere Theories and Universal Algebra. The End.

The aim of this project is to introduce logic students to category theory and to categorical reasoning. This project is a preparation for more advanced study of the field or/and its applications to logic. After the project the students will be able to study (advanced) topics with more classical books like McLane or Adamek et al. The material presented on the project might be particulary useful for the course Capita selecta: Algebra & Coalgebra

In this project we will formalize naive mathematics with the language of category theory. It is worth the effort to study this idea because it provides a unified guide to approaching constructions and problems in the science of space and quantity. We will focus on the notions of diagram, functor, natural transformation, and adjunction; the latter being one of the most powerful tools category theory has introduced to mathematics.

No previous knowledge of category theory is assumed from the students. Neither we assume knowledge of mathematical structures like topological spaces or groups and rings. However, a general culture on ILLC logic is assumed. Basic knowledge on modal logic, Boolean algebras, modal algebras, Kripke frames, first order classical logic, first order structures, or recursion theory will prove to be useful to work out examples and solve exercises.

• The project is worth 6 ECTS (162 hours of work).
• The grading is based on homework assigments.
• In principle, each lecture will have a homework assigment.
• More detailed information can be found on the Assigments page.