Geodesic
The Fermat functors
Theory and applications of categories, Tome 31 (2016), pp. 807-832

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

In this paper, we use some basic quasi-topos theory to study two functors: one adding infinitesimals of Fermat reals to diffeological spaces (which generalize smooth manifolds including singular spaces and infinite-dimensional spaces), and the other deleting infinitesimals on Fermat spaces. We study the properties of these functors, and calculate some examples. These serve as fundamentals for developing differential geometry on diffeological spaces using infinitesimals in a future paper.

Publié le :
Classification : 18F99, 57P99
Keywords: Fermat reals, the adding infinitesimal functor, the deleting infinitesimal functor 
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     author = {Enxin Wu},
     title = {The {Fermat} functors},
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     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2016_31_a27/}
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Enxin Wu. The Fermat functors. Theory and applications of categories, Tome 31 (2016), pp. 807-832. http://geodesic.mathdoc.fr/item/TAC_2016_31_a27/