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A Datalog program can be viewed as a syntactic specification of a functorfrom database instances over some schema to database instances over anotherschema. The same holds more generally for $\exists$Datalog. We establish largeclasses of Datalog and $\exists$Datalog programs for which the correspondingfunctor admits a generalized right-adjoint. We employ these results to obtainnew insights into the existence of, and methods for constructing, homomorphismdualities within restricted classes of instances. We also derive new resultsregarding the existence of uniquely characterizing data examples for databasequeries.

Right-Adjoints for Datalog Programs, and Homomorphism Dualities over Restricted Classes