Isn't this funny tensor product of C and D the pushout of the inclusions of (Ob C x Ob D) into (C x Ob D) and (Ob C x D) --where Ob C is the discrete category with the same objects as C? On Fri, Jul 6, 2012 at 5:13 AM, Ondrej Rypacek <ondrej.rypacek@gmail.com> wrote:
Thanks for all answers and references. It's much appreciated!
Before I tuck in, am I likely to find a definition in terms of a colimit?
Ondrej
On 6 Jul 2012, at 00:42, Mark Weber wrote:
Dear Ondrej and Peter
The fact to which Peter referred, that the tensor product in question
is the unique other symmetric monoidal closed structure on Cat
was proved in the paper [1] F. Foltz, G.M.Kelly, and C. Lair, "Algebraic categories with few biclosed monoidal structures or none", JPAA 17:171-177, 1980
As for the name, this tensor product has been called the "funny tensor product" by some authors. But as I argued in my paper
[2] Free products of higher operad algebras http://arxiv.org/abs/0909.4722
in which such a tensor product is defined for any structure definable by a "normalised higher operad" in the sense of Batanin, the name "free product" is a better choice of terminology.
Mark Weber
-- Omar Antolín Camarena [For admin and other information see: http://www.mta.ca/~cat-dist/ ]