论文标题
最小模型结构
Minimal model structures
论文作者
论文摘要
我们证明，没有设定理论假设，每个可本地呈现的类别C都具有可拖动的合并生成的一类Cofibrations类具有独特的最小（或左）Quillen模型结构。更一般而言，对于C中的任何集合箭头，我们都会在C上构建最小模型结构。我们将其等价类别描述为“最小的cisinski定位器，其中S”。我们的证明依赖于仔细使用胖小对象的论点和J. Lurie的“良好colimits”技术，以及作者先前在组合弱模型类别和半模型类别上的工作。我们还为左半模型类别获得了类似的结果。
We prove, without set theoretic assumptions, that every locally presentable category C endowed with a tractable cofibrantly generated class of cofibrations has a unique minimal (or left induced) Quillen model structure. More generally, for any set S of arrows in C we construct the minimal model structure on C with the prescribed cofibrations and making all the arrows of S weak equivalences. We describe its class of equivalences as the "smallest Cisinski localizer containing S". Our proof rely on a careful use of the fat small object argument and J.~Lurie's "good colimits" technology and on the author previous work on combinatorial weak model categories and semi-model categories. We also obtain similar results for left semi-model categories.
