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From: "Artur Zawlocki" <zawlocki@mimuw.edu.pl>
To: categories@mta.ca
Subject: Re: Grothendieck construction
Date: Wed, 17 Jan 2007 09:47:01 +0100 (CET)	[thread overview]
Message-ID: <18617.7352713004$1241019389@news.gmane.org> (raw)

> Dear All,
>
> Where does the Grothendieck construction come from? What is the original
> 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%C3%A9trie_alg%C3%A9brique):

Grothendieck, Alexandre, Séminaire de Géométrie Algébrique du Bois Marie -
1960-61 - Rev&#234;tements étales et groupe fondamental - (SGA 1) (Lecture
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.
>
>
>





             reply	other threads:[~2007-01-17  8:47 UTC|newest]

Thread overview: 6+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2007-01-17  8:47 Artur Zawlocki [this message]
  -- strict thread matches above, loose matches on Subject: below --
2017-03-13 21:40 Grothendieck Construction Joseph Moeller
2007-01-19 18:44 Grothendieck construction David Espinosa
2007-01-18 19:50 I. Moerdijk
2007-01-17  1:23 wlawvere
2007-01-16 14:17 Gaucher Philippe

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