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Jun 10, 2014 at 3:44 comment added Omar Antolín-Camarena I wonder if the three conditions of preserving colfiltered limits, filtered colimits and weak pullbacks are independent.
Jun 10, 2014 at 2:48 history edited Todd Trimble CC BY-SA 3.0
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Jun 10, 2014 at 2:44 comment added Todd Trimble If you're just interested in the characterization theorem, then it's proved in other places, for example R. Hasegawa, Two applications of analytic functors, Theoret. Comput. Sci. 272 (2002), 113–175. I don't know if Joyal's article has been translated, but if it helps, I am like many people in that I've never really studied French but I can muddle through mathematical French anyway. I think you ought to give it a go; his article is rather beautiful.
Jun 10, 2014 at 2:26 vote accept Brent Yorgey
Jun 10, 2014 at 2:26 comment added Brent Yorgey Thanks! By the way, do you know if there is an English translation of Joyal's article anywhere? Or am I just going to have to bite the bullet and learn some French?
Jun 10, 2014 at 2:19 history answered Todd Trimble CC BY-SA 3.0