Geodesic
Gaps and dualities in Heyting categories
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 1, pp. 9-23.

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We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones.
Classification : 05C65, 05C75, 05C99, 06D20, 18D15
Keywords: Heyting algebras; dualities and gaps; Heyting categories 
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     title = {Gaps and dualities in {Heyting} categories},
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Nešetřil, J.; Pultr, A.; Tardif, C. Gaps and dualities in Heyting categories. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 1, pp. 9-23. http://geodesic.mathdoc.fr/item/CMUC_2007__48_1_a1/