Category Theory: Introduction

This lecture introduces the fundamental concepts of categories and functors, exploring concrete categories, groupoids, and morphisms. It covers the properties of concrete categories, the uniqueness of inverses, and the construction of categories from relations. The lecture also delves into the composition of categories, the minimum number of objects and morphisms in a category, and the uniqueness of inverses. Additionally, it discusses the construction of categories from directed graphs and the associative nature of compositions. The lecture concludes with a detailed examination of exceptional cases in category theory.