The thing about isomorphisms between algebraic structures is that they require a representational+inversible mapping (what you mentioned) that preserves relatio

The thing about isomorphisms between algebraic structures is that they require a representational+inversible mapping (what you mentioned) that preserves relations (something you didn't mention). That distinction is actually relatively important in programming because you might be using something like polymorphism to operate on two representationally equivalent types in different ways. If you have a base class CollidableObject that both PoolBall and GlobOfHoney extend, they could be representationally equivalent (both having two vector member fields, one for Position and one for Velocity) but with different implementations of CollidableObject::HandleCollision(CollidableObject& target) to reflect the fact that PoolBall can elastically collide with certain kinds of targets but GlobOfHoney only collides inelastically. So you'd not want to treat them as isomorphic. I'm mostly just being pedantic but one of my pet peeves is when programmers use terms like Isomorphism or Vector in a way that is partly but not entirely true to the mathematical definition. I think "bijection" is a better term for what you're talking about, because it's both necessary and sufficient for information-preserving mapping between types.