I guess this is a bit of a soft question. Suppose you have a hom of commutative rings with identity $R\to S$, and a hom of $S$ modules $f: M\to N$. Somehow it shouldn't matter whether you localize $f$ in the category of $S$ modules or in the category of $R$ modules (I realize I'm leaving vague the set you're using to localize). What is the correct, most general or most categorical statement of this?
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