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

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