Categorical Analysis

Details Categorical Analysis Categorical Analysis

2001-01-12

arxiv.org/abs/math/0101115v1

Mathematics

Category Theory

27 pages, many figures, AMSLaTeX, written in 1999 - still preliminary

Scientific paper

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.

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