Natural duality

Summary

A natural duality represents each algebra in the quasivariety generated by a finite algebra $M$. The algebra becomes an algebra of continuous structure-preserving maps on a topological structure. The dual of an algebra $A$ is the set of homomorphisms from $A$ to $M$. It is viewed inside a power of a topological structure $\underset{\sim}{M}$ on the same set as $M$. Stone duality for Boolean algebras and Priestley duality for bounded distributive lattices are the model cases. The theory gives general conditions under which such a duality exists. It also tells when the duality is a dual equivalence of categories, a Stone-type duality.