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Can you name some properties of the functor category Funct(R-Mod,S-Mod), where R,S are associative rings with unit?

EDIT: I am sorry for the lack of precision of my (first in MO) question. I was thinking in a sort of Yoneda's Lemma for functors $F\colon R\mbox{-Mod}\to S\mbox{-Mod}$, maybe using tensorizing functors $h_U$ to describe $Nat(h_U,F)$.

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    $\begingroup$ I think it might that your question has been downvoted because it comes off as vague. But I for instance am very ignorant about this category and only recently started reading about Morita theory. So answers would be nice :) $\endgroup$
    – Yosemite Sam
    Jan 28, 2012 at 0:52
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    $\begingroup$ mathoverflow.net/howtoask - what properties? Is it very like a whale? $\endgroup$
    – Yemon Choi
    Jan 28, 2012 at 1:30
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    $\begingroup$ Here is a definite question you might ask: One knows their is a "set"(?) map $ring(S,R)\rightarrow Fun(R-mod,S-mod)$. Other than elements in the image of this map, what else is there? What is a concrete example something not in this image? What are some conditions on $R$ and $S$ for this map to be an isomorphism? Answers to these questions might shed some light on the properties of the category. $\endgroup$
    – Spice the Bird
    Jan 28, 2012 at 3:49
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    $\begingroup$ In Morita theory, you should consider the category of R-S bimodules. Tensoring with a bimodule gives all colimit preserving functors and so in particular all equivalences. Bimodules form a nice abelian category. $\endgroup$
    – Benjamin Steinberg
    Jan 28, 2012 at 4:27
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    $\begingroup$ -1 since still there is no precise question at all. $\endgroup$
    – Martin Brandenburg
    Jan 28, 2012 at 10:05

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