### Lecture 2

Check out the exercises for Lecture 2 (not included in the video lecture) at the end of this post. The rest of the post is mostly based on the video lecture. 2.1. The Big Secret We ended last lecture saying that we should discuss examples of categories, as the next step. The two examples we had in mind had to do with the divisibility relation between numbers and composition of functions. Before discussing these examples, let us step back a bit and ask the question: what is the broad intuition behind the concept of a category -- what sort of phenomena of life/nature/science is it supposed to represent? Let us first answer this question for the concept of a directed graph. Directed graphs arise in life/nature/science as situations where a certain type of objects is identified and we would like to investigate a certain type of relation between these objects. For instance, the objects in question could be natural numbers (i.e., measures of whole quantities) and the relation we may be int