Why is it interesting?

Category theory is a mathematical theory of mathematical theories. This means, category theory is all about the relationship between different mathematical theories.

This helps do understand the connections between different branches of mathematics and helps generalizing them.

Physics involves the crown jewels of modern mathematics, so something deep might be going on, but, second, these insights remain piecemeal. There is a field of mathematics here, another there. One could get the idea that somehow all this wants to be put together into one coherent formal story, only that maybe the kind of maths used these days is not quite sufficient for doing so.

https://physics.stackexchange.com/a/97883/37286

Category theory is an approach to understand these connections and categorise them. In this sense, category theory is a meta-theory of mathematics.

See also: Categorifying Fundamental Physics by John Baez

Layman

Student

• http://math.ucr.edu/home/baez/categories.html
• Categories for the practising physicist by Bob Coecke, Eric Oliver Paquette
• Conceptual Mathematics: A First Introduction to Categories by Lawvere

Researcher

Examples

Example1

Example2:

FAQ

History

This is a point of view that, more or less implicitly, has driven the life work of William Lawvere. He is famous among pure mathematicians as being the founder of categorical logic, of topos theory in formal logic, of structural foundations of mathematics. What is for some weird reason almost unknown, however, is that all this work of his has been inspired by the desire to produce a working formal foundations for physics. (See on the nLab at William Lawvere -- Motivation from foundations of physics).

https://physics.stackexchange.com/a/97883/37286