Introducing categories to the practicing physicist

TL;DR

This paper advocates integrating category theory into the daily practice of physicists, especially quantum physicists and informaticians, emphasizing its relevance to the algebraic structures used in physics.

Contribution

It introduces category theory concepts to physicists in an accessible way, highlighting their importance in understanding the algebra of physics without requiring rigorous mathematical formalism.

Findings

Category theory aligns with the algebraic structures in physics.

Monoidal categories are central to the algebra of practicing physics.

The paper provides an intuitive introduction to category theory for physicists.

Abstract

We argue that category theory should become a part of the daily practice of the physicist, and more specific, the quantum physicist and/or informatician. The reason for this is not that category theory is a better way of doing mathematics, but that monoidal categories constitute the actual algebra of practicing physics. We will not provide rigorous definitions or anything resembling a coherent mathematical theory, but we will take the reader for a journey introducing concepts which are part of category theory in a manner that the physicist will recognize them.