Category Theory For Beginners: Introduction

Richard Southwell introduces the fundamental concepts of category theory, including categories, monoids, and preorders, with connections to programming.

Category theory is close to the perfect language. It can be used to describe many mathematical ideas, and see the relations between them, and their deeper structure. This is the first video in a course where we will carefully introduce the main ideas of category theory, and motivate them with lots of applications. This first video gives the definition of a category and give some motivation for studying the subject. In particular we define a category, give the definition of a monoid, we define a pre-ordered set (preorder), we define the category Set, of sets and functions. We introduce functional programming. We define the final object (terminal object), and explain how the ideas can be used to do set theory without considering the elements within sets directly. Some people have said they want to support my efforts to make educational videos and software, and so I have made a Patreon page patreon.com/richardsouthwell Any support would really help me produce more videos and software.