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Functorial Factorizations in the Category of Model Categories

Applied Categorical Structures, 2021
It is familiar that the category of small categories admits a cofibrantly generated model category structure, called the \textit{canonical model category structure}, whose weak equivalences are the equivalences of categories. \textit{M. Hovey} [Model categories. Providence, RI: American Mathematical Society (1999; Zbl 0909.55001), p.
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Quillen model categories

Journal of K-theory, 2013
AbstractWe provide a brief description of the mathematics that led to Daniel Quillen's introduction of model categories, a summary of his seminal work “Homotopical algebra”, and a brief description of some of the developments in the field since.
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Reedy model categories

1999
This chapter contains an exposition of the Bousfield-Kan model structure on the category cS of cosimplicial objects in simplicial sets, also known as cosimplicial spaces. It appears here as the dual of a Reedy model category structure on the category of simplicial objects sC in a suitable closed model category C.
Paul G. Goerss, John F. Jardine
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