Enriched Grothendieck topologies under change of base

In the presence of a monoidal adjunction F G : U V between locally finitely presentable B\'enabou cosmoi, we examine the behavior of V-Grothendieck topologies on a V-category C, and that of their constituent covering sieves, under the change of enriching category G_* : V-Cat → U-Cat induced by G. We prove in particular that when G is faithful and conservative, any V-Grothendieck topology on C corresponds uniquely to a U-Grothendieck topology on G_*C, and that when G is fully faithful, base change commutes with enriched sheafification in the sense of Borceux-Quinteiro.