Have you ever heard about categories? What are they? What are they useful for?
We will start the following question: take two groups G and H and look at the set of homomorphisms between them. Does this set have a group structure? To answer this question, we will introduce some basic notions of category theory. We will reformulate our question in categorical terms and then see how categories help us solve it. Along the way, we'll define what categories and functors are and look at examples. We’ll actually see that many mathematical objects we know are categories.