Category of differential manifolds with smooth maps

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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.