# Cartesian Factorization Systems and Grothendieck Fibrations

@article{Myers2020CartesianFS, title={Cartesian Factorization Systems and Grothendieck Fibrations}, author={David Jaz Myers}, journal={arXiv: Category Theory}, year={2020} }

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…

## 3 Citations

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