Super, quantum and non-commutative species
Category Theory
2009-05-27 v3 High Energy Physics - Theory
Quantum Physics
Abstract
We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics. Via the usual duality between algebra and geometry, these constructions provide categorifications for various types of affine spaces, thus our works may be regarded as a starting point towards the construction of a categorical geometry.
Cite
@article{arxiv.math/0509674,
title = {Super, quantum and non-commutative species},
author = {Rafael Diaz and Eddy Pariguan},
journal= {arXiv preprint arXiv:math/0509674},
year = {2009}
}
Comments
43 pages, 12 figures