Homotopy theory of spectral categories
نویسندگان
چکیده
منابع مشابه
On the Homotopy Theory of Spectral Categories
Let Sp be the category of symmetric spectra, regarded as having the stable model structure. We prove that the category of small categories enriched over Sp admits a model category structure. The method of proof applies to other categories than symmetric spectra as well, as long as these categories are linked to the category of simplicial sets via a certain strong monoidal Quillen pair.
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Definition 1.1. A weak factorization system (L,R) in a category K consists of two classes L and R of morphisms of K such that (1) R = L , L = R and (2) any morphism h of K has a factorization h = gf with f ∈ L and g ∈ R. Definition 1.2. A model category is a complete and cocomplete category K together with three classes of morphisms F , C and W called fibrations, cofibrations and weak equivalen...
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We give sufficient conditions for the existence of a Quillen model structure on small categories enriched in a given monoidal model category. This yields a unified treatment for the known model structures on simplicial, topological, dgand spectral categories. Our proof is mainly based on a fundamental property of cofibrant enriched categories on two objects, stated below as the Interval Cofibra...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2009
ISSN: 0001-8708
DOI: 10.1016/j.aim.2009.01.014