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arXiv math/0308056math.KTmath.AT
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码下降理论II:相干近似

Codescent theory II: Cofibrant approximations

Paul Balmer, Michel Matthey

摘要:

本文建立了一种在$S$值$C$ -指标图的模型范畴$U_S(C,D)$中产生具有$D$ -弱等价和$D$ -纤维化的协调逼近的一般方法。我们还提出了明确的例子,这样的近似。在这里,$S$是任意共纤生成的单纯模型范畴,而$D\subset C$是小范畴。同伦余限的概念的应用。

英文摘要:

We establish a general method to produce cofibrant approximations in the model category $U_S(C,D)$ of $S$-valued $C$-indexed diagrams with $D$-weak equivalences and $D$-fibrations. We also present explicit examples of such approximations. Here, $S$ is an arbitrary cofibrantly generated simplicial model category and $D\subset C$ are small categories. An application to the notion of homotopy colimit is presented.

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