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
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