Categories enriched in braided tensor categories

There seems to be an interesting gap in the literature on enriched categories --- while monoidal categories enriched in symmetric monoidal categories have been extensively studied (for example in Max Kelly's book), there's a perfectly good notion of a monoidal category enriched in a merely braided monoidal category.

I'll recap last week (I know there will be several participants who missed it), perhaps sketch the classification theorem, or more likely talk about examples.