Dear mathematicians, I have a terminology problem concerning monoidal adjunctions and would therefore like to ask some experts. Let V and W be two symmetric monoidal categories and L: V <--> W :R an adjunction of (lax) symmetric monoidal functors, .i.e. the unit and the counit are monoidal natural transformations. In a previous post, it was pointed out to me that L have to be automatically a strong symmetric monoidal functor then (I do not remember if the monoidal structures have to be closed for this implication). I have read the term 'strong symmetric monoidal adjunction' and it seems to me that this is just a monoidal adjunction with a strong monoidal L. Why is this definition not redundant? I have also read about a 'strict symmetric mnonoidal adjunction'. This confuses me totally, since I have the impression that there is sometimes inconsistency in the use of the term 'strict' and 'strong'. Thank you for any help. Tony [For admin and other information see: http://www.mta.ca/~cat-dist/ ]