In an email to the categories mailing list dated 21 August 2003, Street writes:
- 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.
Is there a reference in the literature for the definition of "$\mathcal V$-category enriched in a monoidal $\mathcal V$-category $\mathcal W$" and proof that it reduces in the manner described?
(Presumably "SLNM420" is the Proceedings of the Sydney Category Theory Seminar 1972/1973, but I could not find a result like this there.)
