Related to Mike and Paul's messages to categories, I had the following observation in my recent draft paper (http://www.kurims.kyoto-u.ac.jp/~hassei/papers/basic.ps.gz "Logical predicates for intuitionistic linear logic", Lemma A.1): Suppose that C and D are symmetric monoidal closed categories and that G:C->D is a symmetric monoidal functor. Moreover suppose that D has pullbacks. Then the comma category (D,G) can be given a symmetric monoidal closed structure, so that the obvious projection (D,G)->C is strict symmetric monoidal closed. I used this (together with the free symmetric monoidal cocompletion) for deriving "logical predicates (logical relations)" for intuitionistic linear type theories, thus in a similar way as Lafont's use of glueing for typed lambda calculi and ccc. In this paper I also have another lemma for glueing symmetric monoidal adjunctions, for interpreting the modality !. I have been wondering if this is a sort of folklore, but never found a reference. Best Regards, Masahito. Masahito Hasegawa Research Institute for Mathematical Sciences Kyoto University Kyoto 606-8502 Japan MAIL: hassei@kurims.kyoto-u.ac.jp URL: http://www.kurims.kyoto-u.ac.jp/~hassei