与谱序列相关的模型结构的一个分配格
A distributive lattice of model structures relating to spectral sequences
AI总结：
本文证明过滤链复形与双复形上的$S$-模型范畴具有左固有、胞腔和稳定性质，利用胞腔化原则建立Quillen等价关系，并构建了由这些模型范畴组成的分配格。
摘要：
Cirici、Egas Santander、Livinet和Whitehouse引入了过滤链复形与双复形上的$S$-模型范畴结构，后由本文作者推广。本文证明它们是左固有、胞腔且稳定的模型范畴。利用这些性质及Greenlees和Shipley的胞腔化原则，证明了一个以从双复形到过滤链的积全化函子为右伴随的伴随关系是Quillen等价。结合过滤链间其他已知的Quillen等价，表明这些模型范畴均呈现相同的同伦范畴。我们还构建了一个分配格，其元素为过滤链复形的$S$-模型范畴。
英文摘要：
The $S$-model category structures on filtered chain complexes and bicomplexes were introduced by Cirici, Egas Santander, Livernet and Whitehouse and later generalised by this author. In this paper we show they are left proper, cellular and stable model categories. We use these properties and the Cellularization Principle of Greenlees and Shipley to show that an adjunction with right adjoint the product totalisation functor from bicomplexes to filtered chains is a Quillen equivalence. Combined with other known Quillen equivalences between filtered chains this shows these model categories all present the same homotopy category. We also construct a distributive lattice whose elements are the $S$-model categories of filtered chain complexes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
