An Introduction to Categories and Sets

In this talk I will give an introduction to Category Theory with the aims of providing a purely categorical proof of the familiar DeMorgan's laws of elementary set theory. Along the way I will introduce the concepts of category, functor, and natural transformation, as well as the universal constructions of product and coproduct. The hope is to convey a sense of the power and generality of these ideas through this particular case study in the humble theorem concerning complements of set unions and intersections.