* Re: Simplicial groups are Kan
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
` (5 subsequent siblings)
6 siblings, 1 reply; 11+ messages in thread
From: Peter May @ 2011-09-12 2:29 UTC (permalink / raw)
To: Michael Barr; +Cc: Categories list
The theorem is due to John Moore, but as far as I remember
he never published his proof. It appeared in mimeographed
notes entitled ``Seminar on algebraic homotopy theory'',
Princeton, 1956. The result is Theorem 17.1 in my 1967 book
``Simplicial objects in algebraic topology'', and the argument
there is based on Moore's notes (Moore was my adviser).
On 9/11/11 7:30 PM, 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/ ]
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
^ permalink raw reply [flat|nested] 11+ messages in thread* Re: Simplicial groups are Kan
2011-09-12 2:29 ` Peter May
@ 2011-09-13 14:22 ` William Messing
0 siblings, 0 replies; 11+ messages in thread
From: William Messing @ 2011-09-13 14:22 UTC (permalink / raw)
To: Peter May; +Cc: Michael Barr, Categories list
John Moore did in fact publish his proof that simplicial groups are
Kan. It is stated as Theorem 3.4 in his paper Semi-Simplicial Complexes
And Postnikov Systems (page 242 of the book, Symposium International De
Topologia Algebraica, 1956 conference, book published in 1958). Moore
refers to the Seminaire Cartan, 1954-55, expose XVIII, where the proof
is given in full as Theorem 3 on page 18-04.
Bill Messing
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* Re: Simplicial groups are Kan
2011-09-12 0:30 Michael Barr
2011-09-12 2:29 ` Peter May
@ 2011-09-12 5:10 ` Fernando Muro
2011-09-12 6:07 ` rlk
` (4 subsequent siblings)
6 siblings, 0 replies; 11+ messages in thread
From: Fernando Muro @ 2011-09-12 5:10 UTC (permalink / raw)
To: Categories list
Théorème 3 in Moore, J. C. "Homotopie des complexes monoïdaux, I"
Séminaire Henri Cartan, 7 no. 2, 1954-1955, Exp. No. 18, 8 p.
http://archive.numdam.org/article/SHC_1954-1955__7_2_A8_0.pdf
On Sun, 11 Sep 2011 20:30:47 -0400 (EDT), 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
>
--
Fernando Muro
Universidad de Sevilla, Departamento de Álgebra
http://personal.us.es/fmuro
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^ permalink raw reply [flat|nested] 11+ messages in thread* Simplicial groups are Kan
2011-09-12 0:30 Michael Barr
2011-09-12 2:29 ` Peter May
2011-09-12 5:10 ` Fernando Muro
@ 2011-09-12 6:07 ` rlk
2011-09-12 6:55 ` Urs Schreiber
` (3 subsequent siblings)
6 siblings, 0 replies; 11+ messages in thread
From: rlk @ 2011-09-12 6:07 UTC (permalink / raw)
To: Michael Barr; +Cc: Categories list
Michael Barr writes:
> I know that is a theorem, due I think to John Moore. Can anyone give me a
> pointer to the original article.
>
> Michael
The result first appeared in
J. C. Moore, Homotopie des complexes monoideaux, I, Seminaire Henri Cartan,
1954-55. See Theorem 3 on p. 18-04.
This is available on the web at
http://archive.numdam.org/article/SHC_1954-1955__7_2_A8_0.pdf
The result became somewhat more widely known as a result of
J. C. Moore, Seminar on algebraic homotopy theory, Mimeographed notes, Princeton
University, Princeton, N. J., 1956
-- Bob
--
Robert L. Knighten
541-296-4528
RLK@knighten.org
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^ permalink raw reply [flat|nested] 11+ messages in thread* Re: Simplicial groups are Kan
2011-09-12 0:30 Michael Barr
` (2 preceding siblings ...)
2011-09-12 6:07 ` rlk
@ 2011-09-12 6:55 ` Urs Schreiber
2011-09-12 8:49 ` Tim Porter
` (2 subsequent siblings)
6 siblings, 0 replies; 11+ messages in thread
From: Urs Schreiber @ 2011-09-12 6:55 UTC (permalink / raw)
To: Michael Barr; +Cc: Categories list
On Mon, Sep 12, 2011 at 2:30 AM, Michael Barr <barr@math.mcgill.ca> wrote:
> I know that is a theorem, due I think to John Moore. Can anyone give me a
> pointer to the original article.
According to
http://ncatlab.org/nlab/show/simplicial+group
this is
J. C. Moore, Algebraic homotopy theory, lecture notes, Princeton
University, 1955–1956
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^ permalink raw reply [flat|nested] 11+ messages in thread* Re: Simplicial groups are Kan
2011-09-12 0:30 Michael Barr
` (3 preceding siblings ...)
2011-09-12 6:55 ` Urs Schreiber
@ 2011-09-12 8:49 ` Tim Porter
2011-09-12 9:35 ` Ronnie Brown
2011-09-12 13:00 ` Tierney, Myles
6 siblings, 0 replies; 11+ messages in thread
From: Tim Porter @ 2011-09-12 8:49 UTC (permalink / raw)
To: Michael Barr; +Cc: Categories list
Quoting Michael Barr <barr@math.mcgill.ca>:
> I know that is a theorem, due I think to John Moore. Can anyone give me a
> pointer to the original article.
>
> Michael
>
>
Dear All,
In Curtis's survey article he gives Kan's paper: A combinatorial
description of homotopy groups, Ann. Math. 67(1958)288 - 312.
Actually I believe that the algorithm that Curtis gives does not work.
That in Peter May's book does.
Tim
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^ permalink raw reply [flat|nested] 11+ messages in thread* Re: Simplicial groups are Kan
2011-09-12 0:30 Michael Barr
` (4 preceding siblings ...)
2011-09-12 8:49 ` Tim Porter
@ 2011-09-12 9:35 ` Ronnie Brown
2011-09-12 13:00 ` Tierney, Myles
6 siblings, 0 replies; 11+ messages in thread
From: Ronnie Brown @ 2011-09-12 9:35 UTC (permalink / raw)
To: Michael Barr; +Cc: Categories list
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/ ]
^ permalink raw reply [flat|nested] 11+ messages in thread* RE: Simplicial groups are Kan
2011-09-12 0:30 Michael Barr
` (5 preceding siblings ...)
2011-09-12 9:35 ` Ronnie Brown
@ 2011-09-12 13:00 ` Tierney, Myles
6 siblings, 0 replies; 11+ messages in thread
From: Tierney, Myles @ 2011-09-12 13:00 UTC (permalink / raw)
To: Michael Barr, Categories list
Mike,
I believe this theorem first appeared in Moore's
1956 Princeton notes "Seminar on algebraic homotopy theory".
Unfortunately I seem to have lost my copy of this, so
I can't really verify it, but I'm pretty sure.
Myles
-----Original Message-----
From: Michael Barr [mailto:barr@math.mcgill.ca]
Sent: Sun 9/11/2011 8:30 PM
To: Categories list
Subject: categories: Simplicial groups are Kan
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/ ]
^ permalink raw reply [flat|nested] 11+ messages in thread