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

From Diffgeom

Line 3: | Line 3: | ||

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

− | The category of differential manifolds | + | 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 | ||

Line 10: | Line 10: | ||

==Functors== | ==Functors== | ||

− | There is a functor from the category of differential manifolds and smooth maps, to the [[tps:category of topological spaces | + | 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. |

## Revision as of 00:43, 2 February 2008

## 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.