Originally Posted by

**HTale** I am stuck by this question,

"In general show that for all $\displaystyle j \in I$ there is a map

$\displaystyle \pi_j : \prod_{i \in I} X_i \rightarrow X_j$

which is the 'projection onto the j-th factor' ".

I'm stuck because I didn't even know you could ask this question; I'm all at sea about how to even do this!

Note, that $\displaystyle \pi_j : A_1 \times A_2 \times \cdots \times A_j \times \cdots \times A_n \rightarrow A_j$, given by $\displaystyle \pi_j(a_1, a_2, \ldots, a_j, \ldots, a_n) = a_j$