The Fermat functors

Enxin Wu

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.

Keywords: Fermat reals, the adding infinitesimal functor, the deleting infinitesimal functor

2010 MSC: 18F99, 57P99

Theory and Applications of Categories, Vol. 31, 2016, No. 28, pp 807-832.

Published 2016-08-26.

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