A Handbook of Model Categories
A Handbook of Model Categories
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模型类别手册
DOI：
10.1007/978-3-030-75035-0
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Scott Balchin
中科院分区：
文献类型：
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作者：
Scott Balchin
这本书的想法是在2017年夏天对麦格理大学进行研究访问时构思出来的。起初，我感兴趣的是收集模型范畴及其各种性质的奇异例子，几乎就像拓扑学中反例的模型范畴版本[331]。这很快就发展成了你面前的手册1。尤其是，书的第二部分实现了这一目标，提供了广泛的模型类别的例子，每一节讲述一个故事，或展示某种现象。为了使这本书自成体系，然后增加了第一部分，其中提供了理论的细节以及例子中提到的各种结构。最后，第三部分由一个易于浏览的表格组成，该表格收集了贯穿第二部分的珍奇之处。因此，在开始阅读本书之前，我建议首先浏览第三部分，以了解其中可以找到什么。我不打算--也不推荐--线性阅读这本书。这里给出的技术成果没有一个是新的。相反，新奇之处在于展示。大部分工作都是在文献的各个角落寻找结果，其中许多对我来说都是新的。因此，在写作过程中，我发现了很多模型范畴的结果。我希望使用这本书的人能像我一样享受体验和学习这一理论的乐趣。这本书的设计是为了补充标准范本的分类文本，而不是取代它们，而是充当配套的卷。在我写作的过程中，有一件事变得很明显，那就是像这样令人困惑的短语
The idea for this book was conceptualized during a research visit to Macquarie University in the summer of 2017. At first, I was interested in collecting exotic examples of model categories and their various properties, almost like a model categorical version of Counterexamples in topology [331]. This soon blossomed into the handbook 1 that you see before you. In particular, Part II of the book realizes this goal, providing a wide range of examples of model categories, with each section telling a story, or exhibiting a certain phenomenon. To make the book self-contained, Part I was then added, which provides details of the theory as well as various constructions referred to within the examples. Finally, Part III consists of an easy-to-navigate table which collects curiosities that can be found throughout Part II. As such, before starting to read this book, I first of all recommend browsing Part III to get a feel of what can be found within. I do not intend—or recommend—that the book is read linearly.None of the technical results presented here are new. Rather, the novelty lies in the presentation. The majority of the work went into searching various corners of the literature to find results, many of which were new to me. Consequently, I discovered a lot of model category results during the process of writing. I hope that people using this book will enjoy experiencing and learning the theory as much as I did. The book has been designed to complement the standard model categorical texts and not to replace them, acting instead as a companion volume. One thing that became apparent to me during the process of writing is how confusing phrases such as