论文标题
组合和易于访问的弱模型类别
Combinatorial and accessible weak model categories
论文作者
论文摘要
在先前的工作中，我们引入了称为弱模型类别的Quillen模型类别的削弱。它们仍然允许模型类别理论的所有常规结构，但在某种意义上更容易构造，并且表现得更好。在本文中，我们继续通过引入组合和可访问的弱模型类别来发展他们的一般理论。我们提供了简单的必要条件，在这些条件下，可以将这种弱模型类别扩展到左和/或右半模型类别。作为应用程序，我们恢复了Cisinski-Olschok理论，并将其推广到弱和半模型类别。我们还为组合和易于访问的弱模型结构的左右Bousfield定位提供了一般存在定理，这些结构与上述结果相结合，为左右与Bousfield组合定位的存在结果和左右半模型类别的左右结果提供了结果，从而概括了先前的Barwick结果。令人惊讶的是，我们表明，任何左或右的Bousfield本地化都始终存在，始终存在，没有适当性假设，并且同时既有左和右半模型类别，又不一定是Quillen模型类别本身。
In a previous work, we have introduced a weakening of Quillen model categories called weak model categories. They still allow all the usual constructions of model category theory, but are easier to construct and are in some sense better behaved. In this paper we continue to develop their general theory by introducing combinatorial and accessible weak model categories. We give simple necessary and sufficient conditions under which such a weak model category can be extended into a left and/or right semi-model category. As an application, we recover Cisinski-Olschok theory and generalize it to weak and semi-model categories. We also provide general existence theorems for both left and right Bousfield localization of combinatorial and accessible weak model structures, which combined with the results above gives existence results for left and right Bousfield localization of combinatorial and accessible left and right semi-model categories, generalizing previous results of Barwick. Surprisingly,we show that any left or right Bousfield localization of an accessible or combinatorial Quillen model category always exists, without properness assumptions, and is simultaneously both a left and a right semi-model category, without necessarily being a Quillen model category itself.
