Re: semi direct product

[metere@mat.unimi.it]

Dear Keith,

This reply to the reply is actually more ambiguous... What do you mean
with "extension"?

Anyway, I find it interesting, in the groupoids case, the paper:

"Categorical non abelian cohomology, and the Schreier theory of groupoids",
V. Blanco, M. Bullejos, E. Faro,

on the arXiv as math.CT/0410202.

Best regards,
Beppe Metere.


Quoting "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.
> > >
> > >
> > >
> > >
> >
> >
>
>
>






Quoting "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.
> > >
> > >
> > >
> > >
> >
> >
>
>
>




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