* "Weakly closed" monoidal bicategories?
@ 2014-05-02 15:40 Mike Stay
2014-05-03 0:36 ` Richard Garner
0 siblings, 1 reply; 2+ messages in thread
From: Mike Stay @ 2014-05-02 15:40 UTC (permalink / raw)
To: categories
In a closed symmetric monoidal bicategory, the categories
Hom(A tensor B, C)
and
Hom(A, hom(B, C))
are equivalent. It occurred to me that one could weaken this
equivalence to a mere adjunction. Looking for references, I found
Lars Birkedal's thesis where he considers "weakly closed partial
cartesian" bicategories.
Are there other references I should be aware of? Thanks!
--
Mike Stay - metaweta@gmail.com
http://www.cs.auckland.ac.nz/~mike
http://reperiendi.wordpress.com
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: "Weakly closed" monoidal bicategories?
2014-05-02 15:40 "Weakly closed" monoidal bicategories? Mike Stay
@ 2014-05-03 0:36 ` Richard Garner
0 siblings, 0 replies; 2+ messages in thread
From: Richard Garner @ 2014-05-03 0:36 UTC (permalink / raw)
To: Mike Stay, categories
Dear Mike,
This paper of Vincent Schmitt involves such a structure on the
2-category of symmetric monoidal categories. I don't think the abstract
structure of which this is an instance is made explicit though.
http://arxiv.org/abs/0711.0324
Richard
On Sat, May 3, 2014, at 01:40 AM, Mike Stay wrote:
> In a closed symmetric monoidal bicategory, the categories
> Hom(A tensor B, C)
> and
> Hom(A, hom(B, C))
> are equivalent. It occurred to me that one could weaken this
> equivalence to a mere adjunction. Looking for references, I found
> Lars Birkedal's thesis where he considers "weakly closed partial
> cartesian" bicategories.
>
> Are there other references I should be aware of? Thanks!
> --
> Mike Stay - metaweta@gmail.com
> http://www.cs.auckland.ac.nz/~mike
> http://reperiendi.wordpress.com
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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