Text this: On co-H-maps to the suspension of the projective plane

 _    _     ______               ___     __   _   
| \  / ||  /_   _//     ___     / _ \\  | || | || 
|  \/  ||   -| ||-     /   ||  | / \ || | '--' || 
| .  . ||   _| ||_    | [] ||  | \_/ || | .--. || 
|_|\/|_||  /_____//    \__ ||   \___//  |_|| |_|| 
`-`  `-`   `-----`      -|_||   `---`   `-`  `-`  
                         `-`