Smooth functor

In category theory, a **smooth functor** often refers to a functor that preserves certain structures in a way analogous to smooth maps between manifolds, though the term can vary based on context. In the context of differential geometry, a smooth functor is typically one that operates between categories of smooth manifolds and smooth maps. A functor between two categories of smooth manifolds is called smooth if it preserves the smooth structure of the manifolds and the smoothness of the maps.