ENRICHED MODEL CATEGORIES AND PRESHEAF CATEGORIES
ENRICHED MODEL CATEGORIES AND PRESHEAF CATEGORIES
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丰富的模型类别和 Presheaf 类别
DOI：
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发表时间：
2011
期刊：
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通讯作者：
Jon P. May
中科院分区：
文献类型：
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作者：
B. Guillou;Jon P. May
我们在一个地方收集了各种已知的和民间传说的结果，丰富了模型范畴理论，并增加了一些新的曲折。中心主题是在给定的V-模型范畴和V中的富化预加重范畴之间构造Quillen附加的一般过程，通常是Quillen等价，其中V是任何好的富化范畴。例如，我们重新推导了Schwede和Shipley的结果，即在更一般的假设下，合理的稳定模型是Quillen等价于预模谱范畴(模谱的别名范畴)。本文给出的一般模型分类结果的技术改进和修改在续集(14，15)中应用于等变上下文。它们必然会在各种其他环境中得到应用。
We collect in one place a variety of known and folklore results in enriched model category theory and add a few new twists. The central theme is a general procedure for constructing a Quillen adjunction, often a Quillen equivalence, between a given V -model category and a category of enriched presheaves in V , where V is any good enriching category. For example, we rederive the result of Schwede and Shipley that reasonable stable model cate- gories are Quillen equivalent to presheaf categories of spectra (alias categories of module spectra) under more general hypotheses. The technical improve- ments and modifications of general model categorical results given here are applied to equivariant contexts in the sequels (14, 15). They are bound to have applications in various other contexts.