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Coproduct , direct sum

  1. Aug 14, 2011 #1
    Hi ,

    This is not a hw problem as I have long passed out of college. I was trying to understand why or where would the problem arise in the definition of the direct sum for the coproduct/direct sum for the set (1, 1, 1, .....) infinite number of times. I was trying to reason out as follows.

    (1, 1, 1, ......)[itex]\rightarrow[/itex] Y

    [itex]\uparrow[/itex]

    f[itex]_{i}[/itex][itex]\rightarrow[/itex] Y


    Pls note that the Y is the same as I cannot write the angular arrow.

    Now if I say that f[itex]_{i}[/itex] acting on (e[itex]_{i}[/itex]) maps it to ( 0, 0, ...1 at the ith coordinate , 0, ....) then what is the place where I am making a mistake. The problem as I see is that either the map from the set (1, 1, 1, ...) to Y is either not unique or map from f[itex]_{i}[/itex][itex]\rightarrow[/itex] Y does not give the same value as the other path. I am really not sure which is the one and why.

    Thx
     
    Last edited: Aug 14, 2011
  2. jcsd
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