?? actually i'm at least momentarily confused ... cocontinuous extension of tensor product as essentialness of geometric morphism in affine case .... ??? ..... ?? then in non-affine case the "essentialness" is still there but the "geometricness" is missing ??? ... ??? .... ?? but then ... ??? where's alleged non-essential geometric morphism here ?? ... ??? ... ???? ....

?? some nefarious fourier duality confusion that i fell for _again_ ?? .... ??? ....

?? hmm, "the partialness of 1) corresponds under theorem 2.1 to the non-essentialness of the co-binary diagonal operation of t(x); this shows that t(x) is totally distributive iff x is affine." .... ?? certainly _something_ is screwed up here .....