• Corpus ID: 220055970

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}
}
  • D. J. Myers
  • Published 24 June 2020
  • Mathematics
  • arXiv: Category Theory
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… 
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These notes were written to accompany a talk given in the Algebraic Topology and Category Theory Proseminar in Fall 2008 at the University of Chicago. We first introduce orthogonal factorization
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All covariantly representable structures of dynamical systems -- including trajectories, steady states, and periodic orbits -- compose according to the laws of matrix arithmetic.
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