Differential restriction categories
Category Theory
2012-08-21 v1
Abstract
We combine two recent ideas: cartesian differential categories, and restriction categories. The result is a new structure which axiomatizes the category of smooth maps defined on open subsets of in a way that is completely algebraic. We also give other models for the resulting structure, discuss what it means for a partial map to be additive or linear, and show that differential restriction structure can be lifted through various completion operations.
Cite
@article{arxiv.1208.4068,
title = {Differential restriction categories},
author = {J. R. B. Cockett and G. S. H. Cruttwell and J. D. Gallagher},
journal= {arXiv preprint arXiv:1208.4068},
year = {2012}
}
Comments
72 pages