not sure exactly what your motivation might have been, but the reason that i started (in fact, about 15 minutes before i read the pdf file that you sent me...) thinking about a similar question is connected with trying to improve the theorem about the ag theory formed by the coherent sheaves over P^n ...
to try to understand these theories more systematically, i've been thinking about them as a functor (in some sense...) of the vector space whose projective space is being considered... one idea along these lines is to consider "the projective space of the generic dualizable object v" ... and to consider whether for example serre's theorem extends in some interesting sense to this generality... thus form the ag theory of graded modules of the symmetric algebra of v* ... ??and so forth ...
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