Elias Loomis the Physicist

Categories for the practising physicist

In this chapter we survey some particular topics in category theory in a somewhat unconventional manner. Our main focus will be on monoidal categories, mainly symmetric ones, for which we propose a physical interpretation. Special attention is given to the category of sets and relations, posetal categories, diagrammatic calculi, strictification, compact categories, biproduct categories and abst...

Elias George Hall

A Call for the Structured Physicist Report.

The Loomis–Sikorski Theorem for EMV -algebras

Recently, in [DvZa], we have introduced EMV -algebras which resemble MV -algebras but the top element is not guaranteed for them. For σ-complete EMV -algebras, we prove an analogue of the Loomis–Sikorski Theorem showing that every σ-complete EMV -algebra is a σ-homomorphic image of an EMV -tribe of fuzzy sets where all algebraic operations are defined by points. To prove it, some topological pr...

Introducing categories to the practicing physicist

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 ...