Manp Is A Concrete Category
Like many categories, the category Manp is a concrete category, meaning its objects are sets with additional structure (i.e. a topology and an equivalence class of atlases of charts defining a Cp-differentiable structure) and its morphisms are functions preserving this structure. There is a natural forgetful functor
- U : Manp → Top
to the category of topological spaces which assigns to each manifold the underlying topological space the underlying set and to each p-times continuously differentiable function the underlying continuous function of topological spaces. Similarly, there is a natural forgetful functor
- U′ : Manp → Set
to the category of sets which assigns to each manifold the underlying set and to each p-times continuously differentiable function the underlying function.
Read more about this topic: Category Of Manifolds
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