Category Theory and Universal Properties

Category theory unifies and formalizes mathematical structures and concepts in a way that various area of interest can be connected. For example, many have learned about sets and functions, vector spaces and linear transformations, and groups and homomorphisms. These and many other mathematical structures can be described in terms of objects and arrows to examine their similarities and their differences. In sum, category theory represents the abstractions of other mathematical concepts, which allow us to describe a mathematical idea without referring to its constructive definition, but instead describing it in terms of the unique properties that it satisfies. In this presentation, we will demonstrate the basic ideas of category theory and then formalize the idea of a universal property.