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Feb 17 at 21:58 comment added Maxime Ramzi The question was about "homotopy limits", I guess I didn't check the Stacks project to see what special case it was. Also I thought I might as well cite the appropriate generality. @Z.M
Feb 17 at 21:17 comment added Z. M This is just a sequential system and I guess that it is much easier than anything using model categories. Namely, you only have to identify countable products and equalizers (or fibers).
Feb 17 at 19:05 history answered Maxime Ramzi CC BY-SA 4.0