Re: filtered colimits

Re: filtered colimits

[Michael Barr]

Although Grothendieck did it only for directed sets and in abelian groups,
once he had done that the extension to sets was obvious and to filtered
categories not much more.  Five years later, when I sat in on Sammy's
course called homological algebra, but really category theory, he had the
full limit notion and I think must have talked about filtered index
categories (although I cannot quite remember it).

Michael

On Thu, 4 Dec 2008, Jiri Adamek wrote:

> I would appreciate knowing the inventor of the concept of
> filtered category, and the first source of the fact that
> filtered colimits commute with finite limits in Set.
>
> Thanks for help,
> Jiri Adamek
>
> xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> alternative e-mail address (in case reply key does not work):
> J.Adamek@tu-bs.de
> xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
>
>

filtered colimits

[Jiri Adamek]

I would appreciate knowing the inventor of the concept of
filtered category, and the first source of the fact that
filtered colimits commute with finite limits in Set.

Thanks for help,
Jiri Adamek

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
alternative e-mail address (in case reply key does not work):
J.Adamek@tu-bs.de
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx