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Building a Model Category out of cofibrations and fibrations

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Seunghun Lee

The purpose of this note is to understand the two out of three property
of the model category in terms of the weak factorization systems. We
will show that if a category with classes of trivial cofibrations,
cofibrations, trivial fibrations, and fibrations is given a simplicial
structure similar to that of the simplicial model category, then the
full subcategory of cofibrant and fibrant objects has the two out of
three property, and we will give a list of necessary and sufficient
conditions in terms of the simplicial structure for the associated
canonical "weak equivalence class" to have the two out of three
property.

Keywords:
Model Category, Weak Factorization Systems, Two out of Three Property

2010 MSC:
18G55

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 36, pp 1163-1180.

Published 2015-09-14.

http://www.tac.mta.ca/tac/volumes/30/36/30-36.pdf

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