While it doesn't fully describe it, his category theory diagram reference seems relevant to me. The stricter of the squares seem to be a homomorphism. But the

While it doesn't fully describe it, his category theory diagram reference seems relevant to me. The stricter of the squares seem to be a homomorphism. But the "looser" ones which don't "preserve structure" after the transformation but "find a new structure" are some of the more interesting ones.