For finite posets R and S, a strong G-scheme exists from R to S if and only if #S(P,R) ≤ #S(P,S) for every finite poset P.
Duffus: Powers of ordered sets
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Strong G-schemes and strict homomorphisms
For finite posets R and S, a strong G-scheme exists from R to S if and only if #S(P,R) ≤ #S(P,S) for every finite poset P.