Functor category dualities for varieties of Heyting algebras (Q1861494)

The theory of multisorted strong dualities is developed, which were treated very briefly by \textit{D. M. Clark} and \textit{B. A. Davey} [Natural dualities for the working algebraist. Cambridge: Cambridge University Press (1998; Zbl 0910.08001)]. It is proved that each finitely generated variety \({\mathcal A}\) of Heyting algebras possesses a multisorted strong duality which in general involves the use of partial operations. The main theorem of the paper says that \({\mathcal A}\) is dually equivalent to a category of functors from \(\text{SI}({\mathcal A})\) (the class of subdirectly irreducible algebras in \({\mathcal A})\) into the category of Boolean spaces.