# Category of differential manifolds with smooth maps

From Diffgeom

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:

- 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.