Left-induced model structures and diagram categories
Left-induced model structures and diagram categories
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左诱导模型结构和图表类别
DOI：
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发表时间：
2014
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通讯作者：
B. Shipley
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作者：
M. Bayeh;K. Hess;V. Karpova;Magdalena Kȩdziorek;E. Riehl;B. Shipley
我们证明了左诱导模型范畴结构的存在性结果，其中图范畴上的内射模型结构是一个重要的例子。我们进一步发展了[9]中的凝聚生成和Postnikov呈递的概念，它们是凝聚生成和细胞呈递的弱形式的对偶。作为例子，对k是域，H是k上的微分分次Hopf代数，我们在增广H-余代数上构造了一个左诱导模型结构，并证明了有限维k-向量空间的有界下链复形范畴具有Postnikov表示.最后，我们研究了（广义）Reedy范畴的生成。在传递中，我们还考虑了凝聚生成，细胞表示，和小对象参数的Reedy图。
We prove existence results a la Jeff Smith for left-induced model category structures, of which the injective model structure on a diagram category is an important example. We further develop the notions of fibrant generation and Postnikov presentation from [9], which are dual to a weak form of cofibrant generation and cellular presentation. As examples, for k a field and H a differential graded Hopf algebra over k, we produce a left-induced model structure on augmented H-comodule algebras and show that the category of bounded below chain complexes of finite-dimensional k-vector spaces has a Postnikov presentation. To conclude, we investigate the fibrant generation of (generalized) Reedy categories. In passing, we also consider cofibrant generation, cellular presentation, and the small object argument for Reedy diagrams.