Introduction to Category Theory and Mathematized Thinking
We will explore how mathematical thought can itself be an object of mathematical study. Much of math considers relationships among objects---category theory can speak abstractly about these relationships without reference to the objects that participate within them. Developing math from this perspective elucidates and formalizes the connections and analogies among seemingly disparate mathematical fields such as algebra, combinatorics, topology, logic, and computation. Furthermore, the symbolic language of category theory can serve as a graphic user interface for doing math by outsourcing reasoning to visual manipulation of diagrams.