We formulate the concept of minimal fibration in the context of fibrations in the model category \({\mathbf {S}}^{\mathcal {C}}\) of \({\mathcal {C}}\)-diagrams of simplicial sets, for a small index category \({\mathcal {C}}\). When \({\mathcal {C}}\) is an EI-category satisfying some mild finiteness restrictions, we show that every fibration of \({\mathcal {C}}\)-diagrams admits a well-behaved minimal model. As a consequence, we establish a classification theorem for fibrations in \({\mathbf {S}}^{\mathcal {C}}\) over a constant diagram, generalizing the classification theorem of Barratt, Gugenheim, and Moore for simplicial fibrations (Barratt et al. in Am J Math 81:639–657, 1959).

中文翻译：

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简单集图中的极小值

我们制定最低纤维化的概念fibrations的模型类的背景\（{\ mathbf {S} ^ {\ mathcal {C}} \）的\（{\ mathcal {C}} \） -diagrams的对于小索引类别\（{\ mathcal {C}} \）的简单集合。当\（{\ mathcal {C}} \\）是满足一些轻微有限性限制的EI类时，我们证明\（{\ mathcal {C}} \）- diagrams的每个纤维化都接受行为良好的最小模型。结果，我们在\（{\ mathbf {S}} ^ {\ mathcal {C}} \）中建立了纤维的分类定理。 在常数图上，推广了Barratt，Gugenheim和Moore的分类定理，用于简单的纤维化（Barratt等人，Am J Math 81：639–657，1959年）。