Corpus ID: 493549

FACTORIZATION SYSTEMS

@inproceedings{Riehl2008FACTORIZATIONS,
  title={FACTORIZATION SYSTEMS},
  author={E. 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
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Abstract A functorial notion of factorization system is introduced and shown to coincide with the appropriate 2-categorical notion of algebra, with respect to the monad on Cat which assigns to aExpand
Lax factorization algebras
Abstract It is shown that many weak factorization systems appearing in functorial Quillen model categories, including all those that are cofibrantly generated, come with a rich computationalExpand
NATURAL WEAK FACTORIZATION SYSTEMS
In order to facilitate a natural choice for morphisms created by the (left or right) lifting property as used in the definition of weak factorization systems, the notion of natural weak factorizationExpand
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An “algebraic” refinement of the small object argument is given, cast in terms of Grandis and Tholen’s natural weak factorisation systems, which rectifies each of these three deficiencies. Expand
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E-mail address: eriehl@math.uchicago.edu
  • E-mail address: eriehl@math.uchicago.edu
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