In mathematics, especially in order theory, a complete Heyting algebra is a Heyting algebra which is complete as a lattice. Complete Heyting algebras are the objects of three different categories; the category CHey, the category Loc of locales, and its opposite, the category Frm of frames. Although these three categories contain the same objects, they differ in their morphisms, and thus get distinct names. Only the morphisms of CHey are homomorphisms 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.
Read more about Complete Heyting Algebra: Definition, Examples, Frames and Locales, Literature
Famous quotes containing the words complete and/or algebra:
“The Good of man is the active exercise of his soul’s faculties in conformity with excellence or virtue.... Moreover this activity must occupy a complete lifetime; for one swallow does not make spring, nor does one fine day; and similarly one day or a brief period of happiness does not make a man supremely blessed and happy.”
—Aristotle (384–322 B.C.)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)