  It is known that factorisation systems in categories can be viewed as unitary
pseudo algebras for the "squaring" monad in Cat.
  We show in this note that an analogous fact holds for proper (i.e., epi-mono)
factorisation systems and a suitable quotient of the former monad, deriving
from a construct introduced by P. Freyd for stable homotopy.
  Structural similarities of the previous monad with the path endofunctor of
topological spaces are considered.
