Introducing categories to the practicing physicist

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.

30 pages and 19 pictures

References in corpus (4)

• Impossibility of deleting an unknown quantum state
• Abstract Physical Traces
• Kindergarten Quantum Mechanics
• On Quantum Operations as Quantum States

Cited by in corpus (13)

• A mathematical theory of resources
• Phase groups and the origin of non-locality for qubits
• Mathematical Foundations for a Compositional Distributional Model of Meaning
• The Frobenius anatomy of word meanings I: subject and object relative pronouns
• Categories for the practising physicist
• Completeness of dagger-categories and the complex numbers
• Teleportation, Braid Group and Temperley--Lieb Algebra
• Quantifying quantum invasiveness
• Knots, Music and DNA
• Applied Category Theory for Genomics -- An Initiative
• A Typedriven Vector Semantics for Ellipsis with Anaphora using Lambek Calculus with Limited Contraction
• Limitations on Cloning in Classical Mechanics
• Applied Categories and Functors for Undergraduates