Hello category theorists, I've been working with tensor products of categories of various degrees of cocompletion. What I mean is that I'm considering categories which are J-cocomplete for some class of small categories J, that is it has all colimits of diagrams for all shapes in J. I know that Kelly gives a tensor product for such things when J is small in section 6.5 of his book on Enriched Category Theory, but I'm working with large J, including when J has all categories, and then we're talking about cocomplete categories. I think these things must have been considered somewhere, and I'm hoping you can help me find a reference. Joe Moeller (He/Him) Graduate Student, Mathematics Department University of California, Riverside [For admin and other information see: http://www.mta.ca/~cat-dist/ ]