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/ ]