what is the inclusion map for $Y$ to $Y$ x $Y$?

Question

I am studying homotopy and homology and one map we have been using is the left and right inclusion maps $i_L$, $i_R$, for example from the space $Y$ to the cartesian product $Y$ x $Y$. Whilst I understand that, for example with the left inclusion map, that the left factor in the cartesian proudct is just a replica of the value taken from $Y$, what happens on the right?

I guess what I am asking is what is the ? in $i_L: x \rightarrow (x,?)$

Answer 1

This is defined in the category of pointed spaces by the map:

$$(Y,y_0) \to (Y\times Y,(y_0,y_0))$$