# Coproduct , direct sum

1. Aug 14, 2011

### Sumanta

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, ......)$\rightarrow$ Y

$\uparrow$

f$_{i}$$\rightarrow$ Y

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

Now if I say that f$_{i}$ acting on (e$_{i}$) 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$_{i}$$\rightarrow$ 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