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I notice several current Wikipedia articles on "homomorphism" avoid using the adjective "homomorphic". (e.g. https://en.wikipedia.org/wiki/Group_homomorphism , https://en.wikipedia.org/wiki/Homomorphism).
Of course the problem with saying "A and B are homomorphic" is that there can be a homomorphism from A to B but no homomorphism from B to A may exist. So it would seem best to only to use the terminology "A is homomorphic to B", which suggests the possibility of an asymmetrical relation. But what do we want that terminology to mean? The natural definition (in my opinion) is that it should mean there is a homomorphism from B to A. However, I've heard people use it to mean that there is a homomorphism from A to B.
Of course the problem with saying "A and B are homomorphic" is that there can be a homomorphism from A to B but no homomorphism from B to A may exist. So it would seem best to only to use the terminology "A is homomorphic to B", which suggests the possibility of an asymmetrical relation. But what do we want that terminology to mean? The natural definition (in my opinion) is that it should mean there is a homomorphism from B to A. However, I've heard people use it to mean that there is a homomorphism from A to B.