I am thinking we have transformations and all forms of relationships on sets. But thinking for an abstract algebraic theoretical session, I pondered on whether its possible to transform (or just relate) a single operation to another?
For example
If I have two groups $(G,*)$ and $(H, \bullet)$ and the isomorphism $$f: G \rightarrow H$$Is it possible to define some form of relationship, say g, such that g focuses on relating "*" and "$\bullet$". If yes, please advise on anyway to do it.