Re: bilax_monoidal_functors?=

[Michael Batanin <mbatanin@ics.mq.edu.au>]

  >> Should we shift the
>> numbers and call category a 3-category?
>
> No, but it seems to me that you are doing something very much like this.

Not at all. It may be was not a good example. A better example would be
categories. If we follow the principle "foo = 1 foo" and want to agree
with historical low dimensional terminology we should call categories
2-sets. Set = 1 Set. So, categories = 2 Set. Nobody will do it I guess.
There are many other examples like stack, gerbes and so on. I agree with
Mike Shulman that this is a byproduct of categorification. But we can
survive with it.

Concerning n-braided categories versus (n+1)-fold categories. Yes, I
would be happy to use (n+1)-fold terminology but it also clashes with
iterated monoidal categories of BFSW as I said.

Michael.


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