Andre wrote:
I want you and everyone know that the definition of a braiding in your notes [...] is wrong. But the definition given in the nLab [...] is correct.
Thanks - I fixed the typo. I don't feel too bad, because the definition in the nLab had just one hexagon axiom until I put in the second one. The Breen-Baez-Dolan Stabilisation Hypothesis is a theorem.
Great. How do you prove it? And which definition of n-category are you using? You write: *If a n-type has the structure of an E(n+2)-space then it has the the
structure of an E(infty)-space (canonically)*
This is a special case of the Stabilisation Hypothesis of Breen-Baez-Dolan;
*If a n-category has the structure of an E(n+2)-category then it has the structure of symmetric monoidal category (canonically)*
(Equivalently, *If a monoidal n-category is (n+1)-braided then it has the structure of symmetric monoidal category (canonically)*)
It is not difficult to verify that these statements are formally equivalent.
The Breen-Baez-Dolan Stabilisation Hypothesis is a theorem.
It seems I understand everything except the last sentence. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]