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We revisit an old assertion due to Rouquier, characterizing the perfectcomplexes as bounded homological functors on the bounded complexes of coherentsheaves. The new results vastly generalize the old statement---first of all theground ring is not restricted to be a field, any commutative, noetherian ringwill do. But the generalization goes further, to the abstract world ofapproximable triangulated categories.

The category $\big[{\mathcal T}^c\big]^{\text{op}}$ as functors on ${\mathcal T}^b_c$