From: john baez Subject: categories: tensor product of categories Date: Tue, 24 Mar 1998 12:25:34 -0800 (PST) Where can I read about the "tensor product" of cocomplete categories? (Hopefully this is a sensible and self-explanatory concept.) Or variations on this theme involving categories with coproducts, or finite colimits, or finite coproducts? Date: Thu, 26 Mar 1998 15:27:09 +1100 (EST) From: maxk@maths.usyd.edu.au (Max Kelly) Subject: categories: Re: tensor product of categories This is in response to John Baez' query: Where can I read about the "tensor product" of cocomplete categories? (Hopefully this is a sensible and self-explanatory concept.) Or variations on this theme involving categories with coproducts, or finite colimits, or finite coproducts? I can think of three things of mine in print which are relevant: \item"{[35]}" (with F. Foltz and C. Lair) Algebraic categories with few monoidal biclosed structures or none, {\it Jour. Pure and Applied Alg.} 17 (1980), 171-177. (the last section or so of) \item"{[41]}" Structures defined by finite limits in the enriched context I, {\it Cahiers de Top. et G\'eom. Diff.} 23 (1982), 3-42. \item"{[52]}" (with G.B. Im) A universal property of the convolution monoidal structure, {\it J. Pure Appl. Algebra} 43 (1986), 75-88. Much of this kind of thing is folklore; when one uses "left adjoint" rather than "cocontinuous", some speak of considering "objects in two categories" - see the first paper above. Max Kelly.