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Fundamentals of Physics and Chemistry of the Atmosphere
-Physics, Topology, Logic and Computation: A Rosetta Stone- by John C. Baez adn Mike Stay
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-Physics, Topology, Logic and Computation: A Rosetta Stone- by John C. Baez adn Mike Stay

Posted on 2012-08-03




Name:-Physics, Topology, Logic and Computation: A Rosetta Stone- by John C. Baez adn Mike Stay
Publish Date: 2009
ISBN: : n/a
Pages: 75 pages
File Type: PDF
File Size: 6 MB
Other Info: JB, MS
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Department of Mathematics, University of California, Computer Science Department, University of Auckland

With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this issue, authors make some of these analogies precise using the concept of -closed symmetric monoidal category-.

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a -cobordism-. Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs.

Contents

1. Introduction

2. The Analogy Between Physics and Topology

Background

Categories

Monoidal Categories

Braided Monoidal Categories

Symmetric Monoidal Categories

Closed Categories

Dagger Categories

3. Logic

Background

Proofs as Morphisms

Logical Theories from Categories

4. Computation

Background

The Typed Lambda Calculus

Linear Type Theories

5. Conclusions

References

with TOC BookMarkLinks



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