---
title: "Physics, Topology, Logic and Computation: A Rosetta Stone"
authors:
  - "John C. Baez"
  - "Mike Stay"
year: 2011
venue: "New Structures for Physics, Lecture Notes in Physics 813"
arxiv: "0903.0340"
doi: "10.1007/978-3-642-12821-9_2"
source: "https://arxiv.org/abs/0903.0340"
topics:
  - category-theory
  - physics
  - monoidal
  - lambda-calculus
  - crossover
seed_rank: 18
seed_batch: "prefill-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 10
cites:
  - title: "Categories for the Working Mathematician (2nd ed.)"
    url: "https://doi.org/10.1007/978-1-4757-4721-8"
    year: 1998
    arxiv: null
    doi: "10.1007/978-1-4757-4721-8"
  - title: "Linear Logic"
    url: "https://doi.org/10.1016/0304-3975(87)90045-4"
    year: 1987
    arxiv: null
    doi: "10.1016/0304-3975(87)90045-4"
  - title: "Computational lambda-calculus and monads"
    url: "https://doi.org/10.1109/LICS.1989.39155"
    year: 1989
    arxiv: null
    doi: "10.1109/LICS.1989.39155"
see:
  - "029-categories-for-the-working-mathematician-2nd-ed"
  - "040-linear-logic"
  - "037-computational-lambda-calculus-and-monads"
---

# Physics, Topology, Logic and Computation: A Rosetta Stone

## One-sentence takeaway

Closed symmetric monoidal categories are the common language in which Feynman diagrams, cobordisms, proofs, and programs are the same pictures — a 73-page dictionary that assumes no prior CT.

## Why it matters here

ano’s typed commands, linear resources, and string-diagram thinking are this Rosetta Stone applied to an engine: compact closed structure is how physics-style wiring becomes a compiler IR.

## Key ideas

- A linear operator is formally like a cobordism; the same string diagrams denote quantum processes, topological cobordisms, sequent proofs, and typed programs.
- The precise setting is a closed symmetric monoidal category: tensor is parallel composition, the internal hom is implication / function type, and cups and caps are cups and caps.
- Table-stakes translations: states ↔ proofs of propositions ↔ programs of a type; entanglement ↔ sharing; the no-cloning theorem ↔ linearity.
- Written as exposition for Coecke’s *New Structures for Physics*; the authors claim no new theorem, only a usable dictionary.
- The last third walks through the quantum-computation and topology sides so a PL reader can see why compact closure is not optional once you want duals.

## Caveats

## Links

- arXiv: [0903.0340](https://arxiv.org/abs/0903.0340)
- PDF: https://arxiv.org/pdf/0903.0340
- DOI: [10.1007/978-3-642-12821-9_2](https://doi.org/10.1007/978-3-642-12821-9_2)