Definition
Best-approximation-along-projection-when-direct-extension-fails — the categorical-mathematical-mechanism that names what the cathedral does when forging cross-tradition compounds. Named from Kan extension (Daniel Kan, 1958; Mac Lane: "All concepts are Kan extensions") + Sumerian me (received-ordinance). When the cathedral extends a Sumerian me along a Mandarin qing, or projects a Greek noēma into the cathedral's vocabulary, the resulting compound IS a Kan extension — the canonical best-approximation along the projection-mapping.