Atlas of Fundamental Concepts

A preorder becomes a thin category, while antisymmetry yields a partial order. Meets and joins produce semilattices and lattices; bounds and distributivity lead toward Boolean and Heyting algebras. Complete Heyting algebras are frames, whose opposites are locales. Boolean and modal algebras support classical and modal semantics; Heyting algebras and Kripke frames organize intuitionistic logic.