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In the first section of the paper "Reconstruction of a variety from the derived category and groups of autoequivalences" of Bondal-Orlov (arXiv:alg-geom/9712029), the "well-known Brown lemma" is referenced several times with the paper "Cohomology theories" of E.H. Brown cited. I have heard of the Brown representability theorem which was proved in this paper, but I don't think this is the result being referenced by B-O. Does anyone know which lemma is being referred to?

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    Maybe section 8 of Keller's [Derived categories and their uses](http://www.math.jussieu.fr/~keller/publ/dcu.pdf) for contains the statements you're after, but I'm not sure if this is exactly what you're looking for. Some of the proofs appear in section 6 of Keller's [Derived categories and universal problems](http://www.math.jussieu.fr/~keller/publ/dcp.pdf) (lemmas 6.5 - 6.7).2012-11-13

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