Differential restriction categories

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 ${\mathbb{R}}^n$ 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.

72 pages

References in corpus (1)

• Restriction categories III: colimits, partial limits, and extensivity

Cited by in corpus (7)

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