Difference between revisions of "Category of differential manifolds with smooth maps"

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{{category}}
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{{category structure on manifolds}}
  
 
==Definition==
 
==Definition==
  
The category of differential manifolds and smooth maps is defined as follows:
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The category of differential manifolds with smooth maps is defined as follows:
  
 
* The objects of the category are [[differential manifold]]s
 
* The objects of the category are [[differential manifold]]s
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==Functors==
 
==Functors==
  
There is a functor from the category of differential manifolds and smooth maps, to the [[tps:category of topological spaces and continuous maps|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.
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There is a functor from the category of differential manifolds and smooth maps, to the [[tps:category of topological spaces with continuous maps|category of topological spaces with 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.

Latest revision as of 19:34, 18 May 2008

This article defines a category structure on manifolds (possibly with additional structure)
View other category structures on manifolds

Definition

The category of differential manifolds with smooth maps is defined as follows:

Functors

There is a functor from the category of differential manifolds and smooth maps, to the category of topological spaces with 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.