  Every Grothendieck fibration gives rise to a vertical/cartesian orthogonal
factorization system on its domain. We define a cartesian factorization system
to be an orthogonal factorization in which the left class satisfies 2-of-3 and
is closed under pullback along the right class. We endeavor to show that this
definition abstracts crucial features of the vertical/cartesian factorization
system associated to a Grothendieck fibration, and give comparisons between
various 2-categories of factorization systems and Grothendieck fibrations to
demonstrate this relationship. We then give a construction which corresponds to
the fiberwise opposite of a Grothendieck fibration on the level of cartesian
factorization systems.
  Apart from the final double categorical results, this paper is entirely
review of previously established material. It should be read as an expository
note.
