From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3578 Path: news.gmane.org!not-for-mail From: "Artur Zawlocki" Newsgroups: gmane.science.mathematics.categories Subject: Re: Grothendieck construction Date: Wed, 17 Jan 2007 09:47:01 +0100 (CET) Message-ID: <18617.7352713004$1241019389@news.gmane.org> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=iso-8859-2 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019389 9327 80.91.229.2 (29 Apr 2009 15:36:29 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:36:29 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Jan 17 04:47:12 2007 -0400 X-Keywords: X-UID: 71 Original-Lines: 39 Xref: news.gmane.org gmane.science.mathematics.categories:3578 Archived-At: > Dear All, > > Where does the Grothendieck construction come from? What is the origina= l > reference? Here is the construction. A standard reference is (after Wikipedia, http://en.wikipedia.org/wiki/Grothendieck's_S%C3%A9minaire_de_g%C3%A9om%C= 3%A9trie_alg%C3%A9brique): Grothendieck, Alexandre, S=E9minaire de G=E9om=E9trie Alg=E9brique du Boi= s Marie - 1960-61 - Revêtements =E9tales et groupe fondamental - (SGA 1) (Lect= ure notes in mathematics 224) (in French). Berlin; New York: Springer-Verlag, xxii+447. ISBN 3540056149. An updated version has been put in the arxiv: http://www.arxiv.org/abs/math.AG/0206203 The construction itself is defined in Section 8, as far as I remember. Artur > > Take a functor H:I-->Cat (the category of small categories) > > The objects are the pairs (i,a) where a is an object of H(i). > A morphism (i,a)-->(j,b) consists of a morphism f:i-->j of I and a > morphism > H(f)(a)-->b of H(j). > > pg. > > >