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

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− | {{category}} | + | {{category structure on diff manifolds}} |

==Definition== | ==Definition== |

## Revision as of 01:36, 28 February 2008

Template:Category structure on diff manifolds

## Definition

The category of differential manifolds with 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 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.