The Stacks project

Remove canonicity

Thanks to ZL
https://stacks.math.columbia.edu/tag/08TB#comment-8295

Fix typo in derived

Thanks to anonymous
http://stacks.math.columbia.edu/tag/070M#comment-2463

K = Rlim truncations iff I = lim I_n

K = Rlim truncations iff I = lim I_n

Lemmas about completion

Does the second lemma also hold if I is not finitely generated?

Please email if you know.

Fix confusion about RF commuting with derived limits

Tags: Added new tags

Producing K-injective resolutions

	Suppose you admit the existence of K-injective resolutions in
	the category of O-modules on a site. Next, suppose you have a
	morphism f of ringed sites and a complex K^* on the source of f
	whose cohomology sheaves are each acyclic for f_*. Then it
	doesn't seem clear to me that R^if_*K^* is just the pushforward
	of the ith cohomology sheaf of K^*. In fact I would bet this is
	wrong in general. (Any example or counter argument welcome.)

	To see what happens we add a lemma that tells you explicitly how
	to compute a K-injective resolution of a complex where now we
	assume that each of the cohomology sheaves has bounded
	cohomological dimension on sufficiently many objects of the
	site.