Re: Alternative closed structure on Cat

["Omar Antolín Camarena" <oantolin@math.harvard.edu>]

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


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