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A b s t r a c t. The purpose of this note is to expose a new way of viewing the canonical extension of posets and bounded lattices. Specifically, we seek to expose categorical features of this completion and to reveal its relationship to other completion processes. The theory of canonical extensions is introduced by Jónsson and Tarski [15, 16] for Boolean(More)
This paper presents a unified account of a number of dual category equivalences of relevance to the theory of canonical extensions of distributive lattices. Each of the categories involved is generated by an object having a 2-element underlying set; additional structure may be algebraic (lattice or complete lattice operations) or relational (order) and, in(More)
Partition-induced natural dl alit& for varieties of pseudo-compicmented distrrbutivc lattices, Discrete Malhematics 113 (1993) 41-58. A natural dl:sitty is obtained for each finitely generated variety B,, (n < CG) of distributive p-algebras. 7 he duality for B,, is based on a schizophrenic object: E:, in B,, is the algebra 2 " @ 1 which gencrates the(More)
The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures(More)