This concept you're describing is formalized in mathematics. In category theory it is called a functor. In haskell it is an actual language primitive also calle

This concept you're describing is formalized in mathematics. In category theory it is called a functor. In haskell it is an actual language primitive also called a functor. Note that a functor, however, is more broad. The relationship between the two "subjects" does not necessarily need to be bijective. It can be one way. There are conversions to new spaces with no direct way to convert back the the original entity in the old space. Quaternions and euler angles are an example of this one way conversion where there are multiple possibilities from euler to quat. What's being talked about here is very different from the concept you describe although they are both part of functional programming.