At a deeper level currying is just a specific application of the Hom-tensor adjunction to the category of Sets. In particular the curried function is equivalent

At a deeper level currying is just a specific application of the Hom-tensor adjunction to the category of Sets. In particular the curried function is equivalent to the original. Partial function mappings is a restriction, and inherently not a injection. That is, generally the partial function is not in an equivalent Hom space to the original function.