If you haven't seen any category theory, you might be interested to know that the diagrams the author draws are valuable and important in modern pure math as well. Those last two diagrams totally capture the idea of what a product or variant (coproduct, in math terminology) is.
In general, there are a lot of algebraic structures whose essence is captured by some diagramatic property like these, such as tensor products or fiber products. They're called universal properties. Unfortunately the wikipedia page looks pretty poorly written, but you might find it interesting nonetheless.
In general, there are a lot of algebraic structures whose essence is captured by some diagramatic property like these, such as tensor products or fiber products. They're called universal properties. Unfortunately the wikipedia page looks pretty poorly written, but you might find it interesting nonetheless.
http://en.wikipedia.org/wiki/Universal_property