Complexes with Homology in a Plump Subcategory

According to (1.7.2), we have then a P-resolution functor which is a IS.-equivalence into D (,4) from its A-subcategory whose objects are bounded-above P-complexes. 

For example, if 17 is a topological space, CMs a sheaf of rings on U, and Tlis the abelian category of (sheaves of) left O-modules, then we can take P to be the full subcategory of A whose objects are all the flat O-modules [H, p. 86, Prop. 1.2]. 

A be a plump subcategory of the abelian category A, i.e., a full subcategory containing 0 and such that for every exact sequence in A 

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