Category Theory Course 2023

Outline:

In this course we will explore various topics in category theory. The choice of topics can range from basic to advanced and will depend on the existing knowledge of the subject among the participants. Category theory provides a unifying language for conceptualising phenomena across different disciplines, including subjects within pure mathematics, as well as some aspects of quantum physics, computer science, biology, and others.

Skills outcome:

This course introduces students to basic concepts of category theory, which are useful when applying category theory as a language of conceptualisation in various disciplines. Upon completing the course, you would have gained the skills of making sense of, working with and applying these concepts.

Prerequisites:

Experience with mathematical thinking and working with a symbolic language (e.g., experience with mathematical formalisms). Anyone interested in the course is advised to look through the notes and videos on https://www.zurab.online/2022/08/category-theory-course-2022.html. 

Dates:

From July 29 till 4 November 2023 (Saturdays 10:00-12:00 South Africa, UTC+2). 

Registration/links

Please complete this if you are taking the course: https://forms.gle/H867JENgw4Zg5CSeA 

Zoom link: https://us06web.zoom.us/j/88223134473?pwd=SENhcHMrMW1IY2w4aEQyTjlBU3cyQT09

WhatsApp link: https://chat.whatsapp.com/K5fCCeO9RoY1fQZqzfzcaV

Method of evaluation:

Students will be assessed based on assignments and presentations.

Lecture 1

Topics covered: the definition of a category, the category of matrices, the category of natural numbers, sum of two objects in a category

Lecture 2

Topics covered: sum of two objects in a category (recap), uniqueness of sum (up to an isomorphism); product of two objects in a category, product of a sequence of objects (briefly), isomorphism and duality (intuitive introduction)

Lecture 3

Topics covered: product and sum in the category of matrices, initial and terminal objects, the category of counting systems (the natural number system as an initial object), the complex number system as an initial object, isomorphism in a category and dual category (formal definitions).

Lecture 4

Topic covered: generalised elements

Lecture 5

Topic covered: equalizers