B. A. Davey and H. Werner developed [Colloq. Math. Soc. János Bolyai 33, 101-275 (1983; Zbl 0532.08003)] a general procedure for creating a natural duality between a prevariety \(A=ISP(\underline P)\) generated by a single algebra \b{P} and a category X of topological structures. In Colloq. Math. Soc. János Bolyai 43, 61-83 (1986; Zbl 0603.08011) and Bull. Aust. Math. Soc. 32, 1-32 (1985; Zbl 0609.08004) they showed how certain natural dualities could be obtained, piggyback- fashion, from existing dualities. This new approach had the great merit of indicating how best to construct X. Among the varieties for which dualities were constructed were Stone algebras, Ockham algebras and the subvarieties \(P_{n,m}\), and certain varieties of pseudocomplemented distributive lattices and Heyting algebras. With the exception of Kleene algebras, all these varieties come within the scope of the Piggyback Duality Theorem.
This paper deals with a generalisation of this duality theory applicable to a wide range of varieties, including the rogue example of Kleene algebras mentioned above.