Strict Model Structures for Pro-categories
نویسنده
چکیده
We show that if C is a proper model category, then the pro-category pro-C has a strict model structure in which the weak equivalences are the levelwise weak equivalences. This is related to a major result of [10]. The strict model structure is the starting point for many homotopy theories of pro-objects such as those described in [5], [17], and [19].
منابع مشابه
Calculating Limits and Colimits in Pro-categories
We present some constructions of limits and colimits in pro-categories. These are critical tools in several applications. In particular, certain technical arguments concerning strict pro-maps are essential for a theorem about étale homotopy types. Also, we show that cofiltered limits in pro-categories commute with finite colimits.
متن کاملModel Structures on pro - Categories
We introduce a notion of a ltered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes the examples of [13], [15], and [16]. We give several examples, including a homotopy theory for G-spaces, where G is a pronite group. The class of weak equivalences is an approximation to the class of underlying weak
متن کاملActions of a separately strict cpo-monoid on pointed directed complete posets
In the present article, we study some categorical properties of the category {$bf Cpo_{Sep}$-$S$} of all {separately strict $S$-cpo's}; cpo's equipped with a compatible right action of a separately strict cpo-monoid $S$ which is strict continuous in each component. In particular, we show that this category is reflective and coreflective in the category of $S$-cpo's, find the free a...
متن کاملA folk model structure on omega-cat
The primary aim of this work is an intrinsic homotopy theory of strict ω-categories. We establish a model structure on ωCat, the category of strict ω-categories. The constructions leading to the model structure in question are expressed entirely within the scope of ωCat, building on a set of generating cofibrations and a class of weak equivalences as basic items. All object are fibrant while fr...
متن کاملVarieties of Cubical Sets
We define a variety of notions of cubical sets, based on sites organized using substructural algebraic theories presenting PRO(P)s or Lawvere theories. We prove that all our sites are test categories in the sense of Grothendieck, meaning that the corresponding presheaf categories of cubical sets model classical homotopy theory. We delineate exactly which ones are even strict test categories, me...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004