Categories as mathematical models

TL;DR

This paper presents category theory as a versatile mathematical modeling framework emphasizing relationships between objects, illustrated through examples like vector spaces, groups, and dynamical systems.

Contribution

It introduces a formal definition of models within category theory and demonstrates its application to various mathematical structures.

Findings

Category theory highlights relationships over objects.

Mathematical objects can be viewed as categorical models.

The framework applies to diverse structures like vector spaces and dynamical systems.

Abstract

Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework that highlights the relationships between objects, rather than the objects in themselves. A working definition of model is given, and several examples of mathematical objects, such as vector spaces, groups, and dynamical systems, are considered as categorical models.