Obstacles to Duality between Classes of Relational Structures
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We prove an algebraic result concerning inverse limits of copowers in anS-class of relational structures of the same (finitary or infinitary) type. Among several applications to the nonexistence of category dualities is the following Theorem: If there exist arbitrarily large measurable cardinals then any classK of relational structures containing a nontrivial objectA and all of its cartesian powers via nonempty index sets will fail to be dual to anyS-class. (No large cardinal assumption is necessary if either there is a finite suchA or ifK consists only of finitary relational structures and contains the elementary class generated byA and its cartesian powers).