is a concrete subcategory of ?-Hom.

Induced substructures correspond to subobjects in ?-Emb. If ? has only function symbols, ?-Emb is the subcategory of monomorphisms of ?-Hom. In this case induced substructures also correspond to subobjects in ?-Hom.

Example

As seen above, in the standard encoding of graphs as structures the induced substructures are precisely the induced

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