[Xy-pic] ugly 2-cells (was: à monsieur Kristoffer Høgsbro Rose)

[Ross Moore]

Hi Kris, Kamel, and others.

On 06/01/2009, at 5:13 AM, Kristoffer H Rose wrote:

> Dear Kamel,
>
> I have looked at the diagram [attached in forwarded message] and I  
> am not sure what you intend to fix, and how to fix it.
>
I think the idea is to make the curved (double) arrows look
like they go from one straight arrow to another.
(A 2-cell is a tranformation from one morphism into another.)
So all that is needed is to adjust the start-point and
end-point of such curved arrows. These positions should relate
to the labels on the straight arrows, but need not be the
exact \POSs defined as these are dropped.

Here is an example of how you can do this, making minimal
changes to the supplied coding (the 3rd in the original PDF):

  {\shorthandoff{;}
   \def\ass{\mathop{\mathrm{ass}}}
  \[\xymatrix{\mathbb{E}\times_{\mathbb{B}}\mathbb{E}\times_{\mathbb 
{B}}\mathbb{E}
  \ar[rr]^{\bigotimes\times 1_{\mathbb{E}}}\ar[d]_{1_{\mathbb{E}} 
\times\bigotimes}
  &&\mathbb{E}\times_{\mathbb{B}}\mathbb{E}\ar[d]^{\bigotimes}="a"\\
  \mathbb{E}\times_{\mathbb{B}}\mathbb{E}\ar[rr]_{\bigotimes}="b"
  &&\mathbb{E}
  \POS"a"*+<2cm>{}+L(.5)="A";"b"*+<2cm>{}+UR(.5)="B";
  \ar@/_/_{\ass}"A";"B"}\]}


The other examples can be adjusted similarly, using
Xy-pic kernel \POS operators to specify the end-points
of each arrow.

> If the issue is placing the labels inside instead of outside the  
> diagram then using ^ instead of _ in the right spot should do it.  
> Otherwise I am unsure what you want to change - maybe someone with  
> actual 2-cell experience can chime in?
>
> Happy New Year,
> Kris
>
> __
> Kristoffer H Rose, ph.d. <krisrose at us.ibm.com> +1(914)784-7642 (fax  
> -6324)
> IBM T.J.Watson Research Center, PO Box 704, Yorktown Heights, NY 10598
>


Hope this helps,

	Ross

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Ross Moore                                       ross at maths.mq.edu.au
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