Homomorphisms of Relational Structures
In model theory, the notion of an algebraic structure is generalized to structures involving both operations and relations. Let L be a signature consisting of function and relation symbols, and A, B be two L-structures. Then a homomorphism from A to B is a mapping h from the domain of A to the domain of B such that
- h(FA(a1,…,an)) = FB(h(a1),…,h(an)) for each n-ary function symbol F in L,
- RA(a1,…,an) implies RB(h(a1),…,h(an)) for each n-ary relation symbol R in L.
In the special case with just one binary relation, we obtain the notion of a graph homomorphism.
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