Bokstedt Neeman Resolutions and HyperExt Sheaves

We call M, which is determined uniquely up to isomorphisms, the homo-topy limit of (13.2) and denote it by holimtj. 

That is, the direct product Fa in C A) is also a direct product in K A). 

D A) (note that the direct product exists, see [37, Corollary 7.10]). 

Lemma 13.6. Let I be a small category, S be a scheme, and let X, G V(I, Sch/5 1. Let F be an object o/C(Mod(X,)). Assume that has locally quasi-coherent cohomology groups. Then the following hold. 

1 Let 3 denote the full subcategory of C(Mod(X,)) consisting of hounded below complexes of injective objects o/Mod(X,) with locally quasi-coherent cohomology groups. There is an 3-special inverse system (/n)nGN with the index set N and an inverse system of chain maps (/ t F 7 ) such that 

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