Erratum to ``Left-determined model categories and universal homotopy theories''
نویسندگان
چکیده
منابع مشابه
Left-determined Model Categories and Universal Homotopy Theories
We say that a model category is left-determined if the weak equivalences are generated (in a sense specified below) by the cofibrations. While the model category of simplicial sets is not left-determined, we show that its non-oriented variant, the category of symmetric simplicial sets (in the sense of Lawvere and Grandis) carries a natural left-determined model category structure. This is used ...
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Several methods for constructing left determined model structures are expounded. The starting point is Olschok’s work on locally presentable categories. We give sufficient conditions to obtain left determined model structures on a full reflective subcategory, on a full coreflective subcategory and on a comma category. An application is given by constructing a left determined model structure on ...
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Model categories were introduced by Quillen [Q] to provide a framework through which one could apply homotopy theory in various settings. They have been astonishingly successful in this regard, and in recent years one of the first things one does when studying any homotopical situation is to try to set up a model structure. The aim of this paper is to introduce a new, but very basic, tool into ...
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Propositions 4.2 and 4.3 of the author’s article (Theory Appl. Categ. 14 (2005), 451-479) are not correct. We show that their use can be avoided and all remaining results remain correct. Propositions 4.2 and 4.3 of the author’s [3] are not correct and I am grateful to J. F. Jardine for pointing it out. In fact, consider the diagram D sending the one morphism category to the point ∆0 in the homo...
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If a Quillen model category can be specified using a certain logical syntax (intuitively, “is algebraic/combinatorial enough”), so that it can be defined in any category of sheaves, then the satisfaction of Quillen’s axioms over any site is a purely formal consequence of their being satisfied over the category of sets. Such data give rise to a functor from the category of topoi and geometric mo...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-08-04727-2