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arXiv · 1208.4068

Differential restriction categories

J. R. B. Cockett·G. S. H. Cruttwell·J. D. Gallagher
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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 $\R^n$ 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.

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J. R. B. Cockett, G. S. H. Cruttwell, J. D. Gallagher. 2012-08-20. Differential restriction categories. https://arxiv.org/abs/1208.4068

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