Abstract: The classical (Bancilhon-Spyratos) correspondence between view update translations and views with a constant complement reappears more generally as the correspondence between update strategies and meet complements in the order based setting of S. Hegner. We show that these two theories of database view updatability are linked by the notion of "lens" which is an algebra for a monad. We generalize lenses from the category of sets to consider them in categories with finite products, in particular the category of ordered sets.