In mathematics, invertible homomorphism

To say that two things are isomorphic is to say that they are the same in some sense. More specifically, in abstract algebra, an isomorphism is a function between two things that preserves the relationships between the parts (see Using the language of category theory, morphisms map to morphisms without breaking composition.

Or consider the operation of adding integers Z. The doubling function φ(x) = 2x maps elements of Z to elements of the even integers 2Z. Since φ(a+b) = 2(a+b) = 2a+2b = φ(a)+φ(b), this is an example of an isomorphism.