Category of differential manifolds with smooth maps

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.