The Stacks project

Double up

Thanks to Manuel Hoff
https://stacks.math.columbia.edu/tag/070L#comment-4337

K = Rlim truncations iff I = lim I_n

Slogan by Bhargav Bhatt
http://stacks.math.columbia.edu/tag/070L#comment-853

LaTeX: Hom and SheafHom

	Introduced the macros

	\def\Hom{\mathop{\rm Hom}\nolimits}
	\def\SheafHom{\mathop{\mathcal{H}\!{\it om}}\nolimits}

	and replaced all the occurences of \text{Hom} and \textit{Hom}
	with these.

Left over limits

	in math mode which didn't have \nolimits or \limits associated
	with them...

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.