Categories

With Jason Erbele and Franciscus Rebro

What do languages and dynamical systems have in common? Can the concepts of theorem and proof be applied to music? How are knots like quantum mechanics? Category theory is an abstract branch of mathematics that builds bridges, called functors, between many fields that don't have any obvious connections.

We will explore some of the properties of categories and their interconnections using graphs. Our goal is to develop the notion of functor in an intuitive way. We will start with understanding sets and how to manipulate them in ways that are suggestive of Category theory, quickly finding that graphs can capture the essence of many interesting and important ideas. With these very visual tools, we will find that functors are fun! Some knowledge of set theory (Math 11 or Math 144) is useful, though not required.

Petri net modified from Till Tantau's excellent TikZ PGF tutorial documentation

An infinite graph
A Petri net, from section 3 of the PGF manual, version 2.10