Difference between revisions of "Category of differential manifolds with smooth maps"
From Diffgeom
(New page: {{category}} ==Definition== The category of differential manifolds and smooth maps is defined as follows: * The objects of the category are differential manifolds * The morphisms of...) 

(No difference)

Revision as of 00:43, 2 February 2008
Definition
The category of differential manifolds and smooth maps is defined as follows:
 The objects of the category are differential manifolds
 The morphisms of the category are smooth maps
Functors
There is a functor from the category of differential manifolds and smooth maps, to the category of topological spaces and continuous maps, that sends a differential manifold to its underlying topological space, and sends a smooth map to the underlying continuous map of topological spaces.