Editing Complete Heyting algebra (section)

{{No footnotes|date=October 2009}}

In [[mathematics]], especially in [[order theory]], a '''complete Heyting algebra''' is a [[Heyting algebra]] that is [[completeness (order theory)|complete]] as a [[lattice (order)|lattice]]. Complete Heyting algebras are the [[object (category theory)|objects]] of three different [[category (category theory)|categories]]; the category '''CHey''', the category '''Loc''' of '''locales''', and its [[opposite (category theory)|opposite]], the category '''Frm''' of frames. Although these three categories contain the same  objects, they differ in their [[morphism]]s, and thus get distinct names. Only the morphisms of '''CHey''' are [[homomorphism]]s of complete Heyting algebras.

Locales and frames form the foundation of [[pointless topology]], which, instead of building on [[point-set topology]], recasts the ideas of [[general topology]] in categorical terms, as statements on frames and locales.