Date of Award

6-2019

Document Type

Open Access

Degree Name

Bachelor of Science

Department

Mathematics

First Advisor

George Todd

Keywords

Category Theory, Universal Property, Topology, Abstract Algebra, Arrow, Functor, Natural Transformation

Abstract

Category theory unifies and formalizes the mathematical structure and concepts in a way that various areas of interest can be connected. For example, many have learned about the sets and its functions, the vector spaces and its linear transformation, and the group theories and its group homomorphism. Not to mention the similarity of structure in topological spaces, as the continuous function is its mapping. In sum, category theory represents the abstractions of other mathematical concepts. Hence, one could use category theory as a new language to define and simplify the existing mathematical concepts as the universal properties. The goal of this thesis is to provide an understanding of the basic category theory and to derive the universal property of certain mathematical concepts, such as the direct product, the quotient group, and the discrete topology. We start with the basic definitions of Category Theory, namely defining category, functor, natural transformation, and the adjoint. After establishing the basic definition, we will study some notable examples, as well as to propose some interesting examples of our own. Built upon the understanding of the definitions and examples, we will discuss some related questions and come to an application of category theory, the universal property.

Download

Share

COinS