Differential Restriction Categories
J.R.B. Cockett, G. S. H. Cruttwell, Jonathan Gallagher · Theory and applications of categories · 2011
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.First author partially supported by