Logic and Foundations Commons^™

Category Theory And Universal Property, Niuniu Zhang

Honors Theses

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 …