Rider to my response to Jean Benabou

[Ross Street <street@ics.mq.edu.au>]

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