Lecture 1: Categories
Write-up of the Lecture (notes for reflection - feel free to interact via comments): 1.1. Directed Graphs The goal of this lecture is to define what a category is and to give examples of categories. To explain what a category is, first let us revisit the notion of a directed graph . The latter is a collection of objects, called vertices of the directed graph, and directed edges (represented as arrows) connecting them. Here is an example: This directed graph has four vertices and various arrows between them. Note that in our notion of a directed graph we allow there to be multiple arrows/edges connecting the same pair of vertices, and even arrows that loop in the same vertex. The contour around the diagram of points and arrows signifies that we want to think of the multitude of constituents of a directed graph (the vertices, the arrows, and the data of which arrow start and ends with which vertex) as a single entity. There can thus be many different directed graphs. Here is an...