If structural relations can be reproduced in a simplified form in a different medium, a model may be constructed. If the second condition holds, then x and y are formally analogous irrespective of their constitution. If both conditions hold, the analogy may be called a homology. Homology implies both substantial and formal analogy, and substantial analogy implies formal analogy, but not conversely. If there is also a homomorphism from y into x, and in addition the two morphisms compensate each other, the analogy is called an isomorphism.
Isomorphism is perfect analogy which implies homomorphism, injective analogy, and plain analogy.