* Good identity
@ 2012-01-26 19:00 David Leduc
2012-01-28 2:11 ` David Leduc
0 siblings, 1 reply; 2+ messages in thread
From: David Leduc @ 2012-01-26 19:00 UTC (permalink / raw)
To: categories
Hi,
Let F, G, and H be composable functors. I can define the canonical
natural transformation from (H o G) o F to H o (G o F) without relying
on the evil fact that (H o G) o F = H o (G o F). I just define it
componentwisely: for each X, I take id_(H(G(F(X)))).
This works in the bicategory of small categories. But now if F, G and
H are 1-cells in any bicategory, how can I define the canonical 2-cell
from (H o G) o F to H o (G o F) without relying on the evil fact that
(H o G) o F = H o (G o F).
Thanks!
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: Good identity
2012-01-26 19:00 Good identity David Leduc
@ 2012-01-28 2:11 ` David Leduc
0 siblings, 0 replies; 2+ messages in thread
From: David Leduc @ 2012-01-28 2:11 UTC (permalink / raw)
To: categories
OK, I found it by myself. I was confused and I could not see the
obvious. For reference, I just have to take the component at (H,G,F)
of the associativity constraint (a natural isomorphism) of the
bicategory.
On 1/26/12, David Leduc <david.leduc6@googlemail.com> wrote:
> Hi,
>
> Let F, G, and H be composable functors. I can define the canonical
> natural transformation from (H o G) o F to H o (G o F) without relying
> on the evil fact that (H o G) o F = H o (G o F). I just define it
> componentwisely: for each X, I take id_(H(G(F(X)))).
>
> This works in the bicategory of small categories. But now if F, G and
> H are 1-cells in any bicategory, how can I define the canonical 2-cell
> from (H o G) o F to H o (G o F) without relying on the evil fact that
> (H o G) o F = H o (G o F).
>
> Thanks!
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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