Dualities for constraint satisfaction problems I

A constraint satisfaction problem for structure B has a duality if the existence of a homomorphism from a given structure A to B is equivalent to the non-existence of a homomorphism to A from a structure belonging to a certain well-behaved class. I will introduce the concepts and the ideas needed to characterize a given type of duality in algebraic, logical and combinatorial languages, and relate it with the complexity of the constraint satisfaction problem.