Canonical extensions and completions of posets and lattices

Abstract

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 The theory of canonical extensions is introduced by Jónsson and Tarski [15, 16] for Boolean algebras with operators. Their approach was based on a complete-lattice theoretic characterisation of the dual space of a Boolean algebra and provides access to the benefits of Stone duality in a uniform