# FACTORIZATION SYSTEMS

@inproceedings{Riehl2008FACTORIZATIONS, title={FACTORIZATION SYSTEMS}, author={Emily Riehl and Emily Riehl}, year={2008} }

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 systems, give a few examples, and prove some basic theorems. Next, we turn to weak factorization systems, which play an important role in the theory of model categories, a connection which we make explicit. We discuss what it means for a weak factorization system to be functorial and observe that… Expand

#### 9 Citations

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This work provides a categorical approach to homomorphism counting based on the concept of polyadic (finite) set and obtains new homomorphicism counting results applicable to a number of infinite structures, such as finitely branching trees and profinite algebras. Expand

Cartesian Factorization Systems and Grothendieck Fibrations

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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… Expand

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E-mail address: eriehl@math.uchicago.edu

- E-mail address: eriehl@math.uchicago.edu

Higher topos theory, preprint available at math.CT/0608040

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