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2021-10 NITheCS Mini-School: Dr. Amartya Goswami and Prof. Zurab Janelidze, Elementary Introduction to Category Theory
2021-10 NITheCS Mini-School
Dr. Amartya Goswami and Prof. Zurab Janelidze

Elementary Introduction to Category Theory

Abstract: The aim of this mini-school is to give a very basic introduction to a branch of mathematics called category theory. Anyone who is familiar with numbers and basic arithmetic operations, and namely, addition and multiplication, will be able to follow at least the first lecture. For the second lecture onward, some encounters with basic mathematical structures, such as vector spaces and groups (nothing more than at the undergraduate level), will be useful. Category theory can be seen as a language that allows one to formalise high-level structural ideas in potentially any subject of study, in a simple mathematical framework, which often leads to revealing essential features of the subject in question, as well as to uncovering new conceptual links between different subjects. This simple framework can be illustrated in terms of the physical world around us, without the need to delve into complex mathematical detail, which makes it possible to start learning category theory without much background in mathematics. Category theory has a dual nature of basic and applied science. As a basic science, it is a vast and thriving discipline of pure mathematics. But, in most cases, the development of this discipline is motivated by its applications, within and outside mathematics. The nature of applications of category theory is, however, different from traditional applied mathematics. If the latter aims to aid one to solve specific problems in the context of a complex system, the former aids one in organising knowledge about the complex system, leading to a better conceptual understanding of the complex system and, at a more basic level, a language for thinking about the complex system. In this mini-school, we will take an in-depth look at the most fundamental components of this language: the notions of category, functor and natural transformation.
Oct 19, 2021 02:00 PM
Oct 26, 2021 02:00 PM
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