Categorical Analysis
Category Theory
2007-05-23 v1 Logic
Abstract
We propose the categorification of the algebraic analysis as the Leibniz 3-category given by generators and relations, including the Leibniz 3-cell relation. The Leibniz category offers the `most general' `(co-)derivation' 3-cell. We outline a program in which every 2-cell related to (or a type of) a Leibniz partial (co-)derivation 3-cell, is translated into an appropriate 2-cell related to the Cartan 3-cell, and vice versa. A model of a non-Leibniz 2-cell responsible for the stochastic calculus must be a ternary operation.
Cite
@article{arxiv.math/0101115,
title = {Categorical Analysis},
author = {Zbigniew Oziewicz and Guilleremo Arnulfo Vazquez Coutino},
journal= {arXiv preprint arXiv:math/0101115},
year = {2007}
}
Comments
27 pages, many figures, AMSLaTeX, written in 1999 - still preliminary