In this paper, we study modules over quotient spaces of certain categorified fiber bundles. These are understood as modules over entwining structures involving a small K-linear category \({\cal D}\) and a K-coalgebra C. We obtain Frobenius and separability conditions for functors on entwined modules. We also introduce the notion of a C-Galois extension \({\cal E} \subseteq {\cal D}\) of categories. Under suitable conditions, we show that entwined modules over a C-Galois extension may be described as modules over the subcategory \({\cal E}\) of C-coinvariants of \({\cal D}\).

中文翻译：

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线性类别和Galois扩展上的交织模块

在本文中，我们研究了某些分类纤维束的商空间上的模块。这些被理解为包含小K线性类别\（{\ cal D} \）和K -coalgebra C的交织结构上的模块。我们获得缠绕模块上函子的Frobenius和可分离性条件。我们还介绍了类别的C -Galois扩展\（{\ cal E} \ subseteq {\ cal D} \）的概念。在合适的条件下，我们证明了在C -Galois扩展上纠缠的模块可以描述为\（{\ cal D} \）的C-协变子\（{\ cal E} \）上的模块。