Localic Map

A map $f:L\to M$ between two Locales is localic when

• $f$ preserves all Meets, and thus has a Left Adjoint by the Adjoint Functor Theorem For Posets.
• The corresponding left adjoint $f_{!}:M\to L$ preserves finite meets.

This is a Vertical Decategorification of a Geometric Morphism.