Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories
Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories
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DOI：
10.14288/1.0340401
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发表时间：
2016-05
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影响因子：
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通讯作者：
H. Nakaoka;Yann Palu
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文献类型：
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作者：
H. Nakaoka;Yann Palu
我们给出了正则范畴和三角范畴的同时推广，它适合于考虑余扭对，我们称之为外三角范畴。三角范畴的扩张闭子范畴是外三角范畴的例子。我们给出了一些余扭偶之间的双射对应，我们称之为Hovey孪生余扭偶，并给出了可容许的模型结构。因此，这些模型结构通过可以被赋予三角结构的同伦范畴将某些局部化与某些理想商联系起来。这给出了一个自然的框架来表示余扭对的约化和突变，既适用于精确范畴，也适用于三角范畴。这些结果可以被看作是对这样一种观点的争论，即外三角范畴是写下既适用于精确范畴又适用于三角范畴(扩张闭子范畴)的证明的一种方便的设置。
We give a simultaneous generalization of exact categories and triangulated categories, which is suitable for considering cotorsion pairs, and which we call extriangulated categories. Extension-closed, full subcategories of triangulated categories are examples of extriangulated categories. We give a bijective correspondence between some pairs of cotorsion pairs which we call Hovey twin cotorsion pairs, and admissible model structures. As a consequence, these model structures relate certain localizations with certain ideal quotients, via the homotopy category which can be given a triangulated structure. This gives a natural framework to formulate reduction and mutation of cotorsion pairs, applicable to both exact categories and triangulated categories. These results can be thought of as arguments towards the view that extriangulated categories are a convenient setup for writing down proofs which apply to both exact categories and (extension-closed subcategories of) triangulated categories.