Geodesic
Differential restriction categories
Theory and applications of categories, Tome 25 (2011), pp. 537-613 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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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Classification : 14A20, 18D10, 18C20, 12H05, 32W99, 58A99
Keywords: Differential restriction categories, Rational functions and the Rational monad, Join completion, Classical completion 
@article{TAC_2011_25_a20,
     author = {J.R.B. Cockett and G.S.H. Cruttwell and J. D. Gallagher},
     title = {Differential restriction categories},
     journal = {Theory and applications of categories},
     pages = {537--613},
     year = {2011},
     volume = {25},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2011_25_a20/}
}
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J.R.B. Cockett; G.S.H. Cruttwell; J. D. Gallagher. Differential restriction categories. Theory and applications of categories, Tome 25 (2011), pp. 537-613. http://geodesic.mathdoc.fr/item/TAC_2011_25_a20/