From: Ronnie Brown <ronnie.profbrown@btinternet.com>
To: Michael Barr <barr@math.mcgill.ca>
Cc: Categories list <categories@mta.ca>
Subject: Re: Simplicial groups are Kan
Date: Mon, 12 Sep 2011 10:35:10 +0100 [thread overview]
Message-ID: <E1R3HCt-0003mU-6g@mlist.mta.ca> (raw)
In-Reply-To: <E1R2w5a-00089H-E4@mlist.mta.ca>
The reference is included in this review *MR1173825 *of the cubical case.
Tonks, A. P.
<http://0-ams.mpim-bonn.mpg.de.unicat.bangor.ac.uk/mathscinet/search/publications.html?pg1=IID&s1=325533>(4-NWAL)
<http://0-ams.mpim-bonn.mpg.de.unicat.bangor.ac.uk/mathscinet//search/institution.html?code=4_NWAL>
Cubical groups which are Kan.
/J. Pure Appl. Algebra/
<http://0-ams.mpim-bonn.mpg.de.unicat.bangor.ac.uk/mathscinet/search/journaldoc.html?cn=J_Pure_Appl_Algebra>
81
<http://0-ams.mpim-bonn.mpg.de.unicat.bangor.ac.uk/mathscinet/search/publications.html?pg1=ISSI&s1=118323>(1992),
<http://0-ams.mpim-bonn.mpg.de.unicat.bangor.ac.uk/mathscinet/search/publications.html?pg1=ISSI&s1=118323>no.
1,
<http://0-ams.mpim-bonn.mpg.de.unicat.bangor.ac.uk/mathscinet/search/publications.html?pg1=ISSI&s1=118323>
83–87.
<http://0-ams.mpim-bonn.mpg.de.unicat.bangor.ac.uk/mathscinet/search/mscdoc.html?code=55U10,%2818D35,18G30%29><javascript:openWin('http://unicat.bangor.ac.uk:4550/resserv',
'AMS:MathSciNet',
'atitle=Cubical%20groups%20which%20are%20Kan&aufirst=A.&auinit=AP&auinit1=A&auinitm=P&aulast=Tonks&coden=JPAAA2&date=1992&epage=87&genre=article&issn=0022-4049&issue=1&pages=83-87&spage=83&stitle=J.%20Pure%20Appl.%20Algebra&title=Journal%20of%20Pure%20and%20Applied%20Algebra&volume=81')>
The author shows that group objects in the category of cubical sets with
connections [R. Brown and P. J. Higgins, J. Pure Appl. Algebra 21
(1981), no. 3, 233--260; MR0617135 (82m:55015a)
<http://0-ams.mpim-bonn.mpg.de.unicat.bangor.ac.uk/mathscinet/search/publdoc.html?r=1&pg1=CNO&s1=617135&loc=fromrevtext>]
satisfy the Kan extension condition. This is a very nice correspondence
with the simplicial case [J. C. Moore, in Séminaire Henri Cartan de
l'Ecole Normale Supérieure, 1954/1955, Exp. No. 18, Secrétariat Math.,
Paris, 1955; see MR0087934 (19,438e)
<http://0-ams.mpim-bonn.mpg.de.unicat.bangor.ac.uk/mathscinet/search/publdoc.html?r=1&pg1=CNO&s1=87934&loc=fromrevtext>].
Ronnie
On 12/09/2011 01:30, Michael Barr wrote:
> I know that is a theorem, due I think to John Moore. Can anyone give me a
> pointer to the original article.
>
> Michael
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2011-09-12 9:35 UTC|newest]
Thread overview: 14+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-09-12 0:30 Michael Barr
2011-09-12 2:29 ` Peter May
2011-09-13 14:22 ` William Messing
2011-09-12 5:10 ` Fernando Muro
2011-09-12 6:07 ` rlk
2011-09-12 6:55 ` Urs Schreiber
2011-09-12 8:49 ` Tim Porter
2011-09-12 9:35 ` Ronnie Brown [this message]
2011-09-13 15:12 ` Simplicial versus (cubical with connections) Marco Grandis
[not found] ` <BDF51495-03DB-4725-8372-094AD1608A11@dima.unige.it>
2011-09-13 16:58 ` Ronnie Brown
2011-09-14 7:08 ` Jonathan CHICHE 齊正航
2011-09-12 13:00 ` Simplicial groups are Kan Tierney, Myles
2011-09-13 1:33 Fred E.J. Linton
[not found] <615PimBGm3072S04.1315877592@web04.cms.usa.net>
2011-09-13 9:01 ` Ronnie Brown
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