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/ ]