Representable functors

in category theory, a theorem that embeds a locally small category into a category of functors

functor F: C → Set to the category of sets, naturally isomorphic to a hom-functor hom(X, –) for some object X in C

topological space equipped with a principal bundle with the property that any principal bundle (with the same fiber group) over a paracompact manifold is isomorphic to a pullback of the principal bundle over this topological space