Take the 2-minute tour ×  I've been reading Ravi Vakil's notes
on algebraic geometry notes and am having a hard time connecting
the standard definition of the localization of a module to the
definition in terms of universal properties (page 24).  Can
anybody either explain the connection or provide some kind of
'roadmap' of the material necessary to understand this
connection?  I apologize if this question is vague or unclear.
EDIT: This is an attempt to reformulate my original question to
make it more precise:  Suppose we did not know the definition of
the localization of a module and we just saw the diagram
presented on page 24, how do we recover the usual definition and
how do we determine that anything else satisfying those
properties is isomorphic to the usual definition?  share|improve
this question Sorry, I edited the link to go directly to the
pdf. it should work now –  WWright Sep 11 '10 at 21:53 Isn't
this the content of exercise 2.3.E? –  Robin Chapman Sep 11 '10
at 21:55 I guess. I think I might