Re: Alternative closed structure on Cat

[Ondrej Rypacek <ondrej.rypacek@gmail.com>]

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



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