A smooth version of the Zariski topos
The category M of (finite-dimensional) smooth manifolds has two limitations: it is not Cartesian closed (in particular, the space of maps between two objects need not be a smooth manifold); there is no convenient language to describe things in the ``infinitely small''. Non- standard analysis initiated by A. Robinson addresses the second limitation, and the theory of differentiable spaces of Chen and the theory of convenient vector spaces of Fröhlicher, Kriger, and others address the first limitation. The aim of the paper under review is to construct a Cartesian closed category L containing M as in the previous approaches. In addition to this, L contains nilpotent and invertible infinitesimals and infinitely large natural numbers. Moreover, L is a Grothendieck topos.
category of finite-dimensional smooth manifolds
scientific article; zbMATH DE number 4057751
scientific article