For the robot to ever make it to (1,1) there would have to be a sequence of the following moves ending on (1,1) from the origin (0,0): b and c have an analagous problem, moving continually up the ...

$\exists h: B \rightarrow A. f \circ h = id_B$ **NB**: If $f$ is bijective and $g \circ f = id_A$ and $f \circ h = id_B$ then $h=g$ $g \circ f \circ h$: $g \circ f ...