Dear All Is there a name for and what is known about the tensor product of ordinary categories which looks like the underlying 1-category of Gray's (Gray) tensor product? Explicitly, roughly: - objects of C \otimes D are pairs (c,d) , c object of C , d an object of D - arrows alternating lists of arrows from C and D, i.e. they are generated by (f,d) : (c,d) -> (c',d) for f : c -> c', (c,g) : (c,d) -> (c,d') for g : d -> d' and modulo the equations: (f',d) . (f, d) = (f'f, d), (c,g') . (c,g) = (c,g'g), and identities, left and right unit laws and associativity in each component separately. And is the category of categories with respect to this tensor closed ? Thank you! Ondrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]