I just finished up my rather experimental introductory category theory class. I’m sure it’s probably a bad idea to teach basic category theory to 16-year olds, but it actually went pretty well. My goal was to get the students to understand the idea of a universal construction by discussing products, coproducts, initial, and final objects in some very simple examples. And I think most people in the class understood what was going on.
Yesterday I was talking about products in categories coming from posets. That is, the objects are elements of your poset, and there exists exactly one morphism when . The first example I did was the positive integers under divides. So I took two objects, 7 and 5, and asked what their product was. Eventually they get the right answer, so I write the answer on the board. Suddenly their are flashes going off around me from the students digital cameras. At this point I realize I’ve just written: