forgot password?
register here
Research articles
  search articles
  reviews guidelines
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
Members: 2980
Articles: 2'029'581
Articles rated: 2577

19 January 2021
  » arxiv » math.QA/0004133

 Article overview

From Finite Sets to Feynman Diagrams
John C. Baez ; James Dolan ;
Date 20 Apr 2000
Subject Quantum Algebra; Category Theory; Combinatorics; History and Overview | math.QA math.CO math.CT math.HO
Abstract`Categorification’ is the process of replacing equations by isomorphisms. We describe some of the ways a thoroughgoing emphasis on categorification can simplify and unify mathematics. We begin with elementary arithmetic, where the category of finite sets serves as a categorified version of the set of natural numbers, with disjoint union and Cartesian product playing the role of addition and multiplication. We sketch how categorifying the integers leads naturally to the infinite loop space Omega^infinity S^infinity, and how categorifying the positive rationals leads naturally to a notion of the `homotopy cardinality’ of a tame space. Then we show how categorifying formal power series leads to Joyal’s `especes des structures’, or `structure types’. We also describe a useful generalization of structure types called `stuff types’. There is an inner product of stuff types that makes the category of stuff types into a categorified version of the Hilbert space of the quantized harmonic oscillator. We conclude by sketching how this idea gives a nice explanation of the combinatorics of Feynman diagrams.
Source arXiv, math.QA/0004133
Services Forum | Review | PDF | Favorites   
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
of broad interest:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser CCBot/2.0 (
» my Online CV
» Free

News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2021 - Scimetrica