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Every Grothendieck fibration gives rise to a vertical/cartesian orthogonalfactorization system on its domain. We define a cartesian factorization systemto be an orthogonal factorization in which the left class satisfies 2-of-3 andis closed under pullback along the right class. We endeavor to show that thisdefinition abstracts crucial features of the vertical/cartesian factorizationsystem associated to a Grothendieck fibration, and give comparisons betweenvarious 2-categories of factorization systems and Grothendieck fibrations todemonstrate this relationship. We then give a construction which corresponds tothe fiberwise opposite of a Grothendieck fibration on the level of cartesianfactorization systems.  Apart from the final double categorical results, this paper is entirelyreview of previously established material. It should be read as an expositorynote.

Cartesian Factorization Systems and Grothendieck Fibrations