Re: semi direct product

["Dr. Keith G. Bowden" <k.bowden@physics.bbk.ac.uk>]

Dear Bill,

Your reply is slightly ambiguous.

Do you mean that you call it the semidirect product by extension of the
semi-direct product in group theory?

Regards,
Keith Bowden


----- Original Message -----
From: <wlawvere@buffalo.edu>
To: <categories@mta.ca>
Sent: Wednesday, January 17, 2007 1:23 AM


> Because Grothendieck made many constructions that
> became iconic, the terminology is ambiguous.
> I call this construction
>       "the Grothendieck semi-direct product"
> because the formula for composition of these
> morphisms is exactly the same as in the very special
> case where I is a group.
> Of course the result of the construction is a single
> category "fibered" over I and every fibred category
> so arises.
> The original example for me (1959) was that from
> Cartan-Eilenberg where I is a category of rings and
> H(i) is the category of modules over i.  Because
> J. L. Kelley had proposed "galactic" as the analogue
> at the Cat level of the traditional "local" at the level
> of a space, I called such an H a "galactic cluster" .
> The "fibration' terminology  and the accompanying
> results and definitions for descent etc were presented
> by AG in Paris seminars in the very early 1960's and
> can probably be accessed elecronically now.
>
> Best wishes
> Bill
>
> Quoting Gaucher Philippe <Philippe.Gaucher@pps.jussieu.fr>:
>
> > 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.
> >
> >
> >
> >
>
>