BUILDING A MODEL CATEGORY OUT OF COFIBRATIONS AND FIBRATIONS : THE TWO OUT OF THREE PROPERTY FOR WEAK EQUIVALENCES
BUILDING A MODEL CATEGORY OUT OF COFIBRATIONS AND FIBRATIONS : THE TWO OUT OF THREE PROPERTY FOR WEAK EQUIVALENCES
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用共纤维和纤维构建模型类别：弱等价性的三个属性中的两个
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Seunghun Lee
中科院分区：
文献类型：
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作者：
Seunghun Lee
本文的目的是利用弱分解系统来理解模型范畴的三取二性质。我们将证明，如果一个具有平凡上纤维化，上纤维化，平凡纤维化和纤维化类的范畴被赋予一个与单纯模型范畴类似的单纯结构，那么凝聚和凝聚对象的全子范畴具有三分之二的性质，我们将给出一个列表的必要条件和充分条件的单纯结构的相关规范的“弱等价类”拥有三分之二的财产
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.