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From: Andre Joyal <joyal.andre@uqam.ca>
To: "Toby Bartels" <toby@ugcs.caltech.edu>, "categories" <categories@mta.ca>
Subject: Re: Q about_monoidal_functors?
Date: Fri, 7 May 2010 22:59:41 -0400	[thread overview]
Message-ID: <E1OAsRA-0001ZG-Ht@mailserv.mta.ca> (raw)
In-Reply-To: <E1OAWlO-0001d8-QK@mailserv.mta.ca>

Dear Toby,

Looping and delooping operations can be applied to spaces
and to maps between spaces. 
We should use a similar terminology for spaces and maps.
For example:

E-n space <--> E-n map


Also for (higher) categories and functors. 

monoidal category <---> monoidal functor
braided monoidal category <----> braided monoidal functor
2-braided monoidal category <--> 2-braided monoidal functor
3-braided monoidal category <--> 3-braided monoidal functor
......
......
......

symmetric monoidal category <--> symmetric monoidal functor


A (n+1)-braided monoidal n-category is symmetric by 
the stabilisation hypothesis. 
I believe that a (n+1)-braided monoidal functor 
between (n+1)-braided monoidal n-categories is symmetric. 
Is this part of the official stabilisation hypothesis?

Best,
André 


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


  reply	other threads:[~2010-05-08  2:59 UTC|newest]

Thread overview: 5+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2010-05-07  1:01 Q. about monoidal functors Fred E.J. Linton
2010-05-07 19:48 ` Toby Bartels
2010-05-08  2:59   ` Andre Joyal [this message]
2010-05-09  5:54     ` Q about_monoidal_functors? Toby Bartels
2010-05-13  1:46   ` wrong axioms Andre Joyal

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