2 Categories

With the ideas of set and functions in hand, we move on to the world of categories. Section 2.1 begins with a formal definition of categories. It then proceeds to list a giant stack of examples of categories from all over. In Section 2.2, we discuss some simple properties of morphisms in categories. We elaborate on some simple categories related to a category in Section 2.3. The chapter ends with Section 2.4, which is a mini-course that teaches the basics of linear algebra. The study of linear algebra is essentially an in-depth exploration of the category of vector spaces.