 Although philosophers have focused on isomorphism, other morphisms such as monomorphism (i.e., an injective homomorphism where some elements in the co-domain remain unmapped from the domain) might also be interesting to investigate, especially for embedding data (i.e., the domain) into rich theoretical structures (i.e., the co-domain). To complete the visualization above, an epimorphism is a surjective homomorphism, and an endomorphism is a mapping from a structure to itself, although it need not be a symmetrical—i.e., invertible—mapping, which would be an automorph. 