Re: Good identity

[David Leduc <david.leduc6@googlemail.com>]

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!
>


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