Locale

A locale is a "Frame with an attitude". Much like Inflattices and Suplattices, the data contained in a locale and a frame is the same; what differs are the morphisms. A morphism of frames is the obvious one that preserves finite Meets and infinitary Joins. Conversely, a Localic Map is a morphism in the Opposite of the category of Frames. This gives locales a topological rather than algebraic flavor.