Dear Jean After seeing both Brian and Max in the last two days, I would like to add two remarks to my last message. 1) Brian pointed out that you did not ask for your base V to be closed which is assumed in his paper in SLNM137. However, this is not really a restriction: just embed V in its presheaves with convolution closed monoidal structure. 2) Max reminded me of his old result (not in the LaJolla Proceedings, but known soon after) that a monoidal V-category is none other than a monoidal category W with a "normal" monoidal functor W --> V. (Normal here means that the unit is preserved.) I think this was mentioned by Max somewhere in the literature but I cannot remember where; possibly SLNM420. The good thing about it is that V-categories enriched in the monoidal V-category W turn out to be mere W-categories. An example is the monoidal category W = DGAb of chain complexes of abelian groups; it can be regarded as a monoidal additive category (that is, enriched in abelian groups V = Ab) or as a mere monoidal category; categories enriched in the latter are automatically additive. Best wishes, Ross