subgraphs. However, a homomorphism between graphs is the same thing as a homomorphism between the two structures coding the graph. In the example of the previous section, even though the subgraph H of G is not induced, the identity map id: H -> G is a homomorphism. This map is in fact a monomorphism in the category ?-Hom, and therefore H is a subobject of G which is not an induced substructure.

Homomorphism problem