Dualities and algebras with a near-unanimity term

Let P be a finite relational structure that admits a (k +  1)-ary nearunanimity polymorphism. Then the NU Duality Theorem tells us that the algebra, whose operations are the polymorphisms of P, is dualisable with a dualising alter ego given by. We show that a more efficient alter ego can be obtained by using obstructions, as introduced by Zádori. We show that in the case that P is an ordered set (and therefore is an order-primal algebra), the duality that we obtain is strong. We close the paper by showing that if P is a finite fence, then our duality is optimal.