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From: Gaucher Philippe <Philippe.Gaucher@pps.jussieu.fr>
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Subject: Grothendieck construction
Date: Tue, 16 Jan 2007 15:17:02 +0100
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Dear All,

Where does the Grothendieck construction come from ? What is the original 
reference ? Here is the construction.

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.