Given a symmetric closed monoidal category , a -enriched category with underlying ordinary category and a subcategory of containing the identities of , H. Wolff defines the corresponding theory of localizations.
While Wolff in principle defines localizations more generally, most of the theory is developed for reflective localizations, i.e. when the counit of the 2-adjunction is iso of -categories. For such a -enriched category ,
consider reflective -localizations which preserve finite limits of the enriched category of presheaves , and relate them to an enriched version of Grothendieck topology on , and to a “universal closure operation” on .