Bilimit question

Bilimit question

[Alex Hoffnung]

Dear List,

The weakest form of limits in a bicategory are defined by equivalences of
hom-categories in place of the slightly more strict version defined by
isomorphisms.  Then the process of defining a monoidal structure on a
bicategory with finite products takes on a slightly different flavor in each
case.

In the weak case, given a pair of 1-cells one must *choose* a monoidal
product, whereas in the latter case, a *unique choice* of monoidal product
can be obtained from the one-dimensional aspect of the universal property.

I would guess that in the former case, one should not worry too much about
how to choose the product 1-cells, since the universal property will come to
the rescue when checking that one has indeed defined a monoidal structure on
the bicategory.

Does anyone know of a reference which proves something along these lines?

Best,
Alex


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Re: Bilimit question

[Nick Gurski]

Alex-
The reference you are looking for is Cartesian Bicategories II by
Carboni, Kelly, Walters, and Wood.  Here is a link to the .pdf on the
TAC homepage.
http://www.tac.mta.ca/tac/volumes/19/6/19-06.pdf
Nick


Alex Hoffnung said the following on 23/11/2010 00:44:
> Dear List,
>
> The weakest form of limits in a bicategory are defined by equivalences of
> hom-categories in place of the slightly more strict version defined by
> isomorphisms.  Then the process of defining a monoidal structure on a
> bicategory with finite products takes on a slightly different flavor in each
> case.
>
> In the weak case, given a pair of 1-cells one must *choose* a monoidal
> product, whereas in the latter case, a *unique choice* of monoidal product
> can be obtained from the one-dimensional aspect of the universal property.
>
> I would guess that in the former case, one should not worry too much about
> how to choose the product 1-cells, since the universal property will come to
> the rescue when checking that one has indeed defined a monoidal structure on
> the bicategory.
>
> Does anyone know of a reference which proves something along these lines?
>
> Best,
> Alex
>


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