Re: bilax monoidal functors

[Toby Bartels <toby+categories@ugcs.caltech.edu>]

Michael Batanin wrote:

>Dear John and Andre,

>I am using a mixture of your terminologies:
>  monoidal = 1-braided
>  braided = 2-braided
>  sylleptic = 3-braided
>......

I think that this terminology is dangerous.

While there is a debate to be had over which is better:
John's "k-tuply monoidal" or André's "k-braided monoidal",
the good thing about either of them is that you can understand them
without having to be told precisely how the numbering works,
as long as you follow the rule that "1-foo" = "foo".
So while I also prefer John's numbering to André's,
I'm happy to use either and have had occasion to use both.
But mixing John's numbering with André's terminology would confuse me.

Sometimes the "1-foo" = "foo" rule is violated.
I was very confused when I first saw "n-connected space";
I'd have understood "n-simply connected space" right away.
I tend to think that a lot of established names are badly numbered,
including "n-category" which may be the most basic on a categories list,
but it doesn't really cause any problems as long as "1-foo" = "foo".


--Toby


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]