V-localizations andV-Kleisli algebras

We prove a pushout theorem for localizations and Kleisli categories over a symmetric monoidal closed categoryV. That is, suppose is aV-localizable subcategory of aV-categoryA and thatT=(T,,) is aV-monad onA. Then under suitable relations betweenT and we show that there is aV-monadT induced onA-¹] such that the Kleisli category ofT is the pushout of the localization functor :AA-¹] and the free functor F:AK(T). Consequently,K(T)K(T) S-¹] for some S K(T). We give several examples of this situation.