# If 2 spaces are homotopy equivalent, then their fundamental group is the same

If 2 spaces are homotopy equivalent, then their fundamental group is the same

Is this true ?

Let

$f:X\rightarrow Y$$\quad$$g:Y\rightarrow X$ s.t.

$f\circ g\simeq id_Y$$\quad$$g\circ f\simeq id_X$

then