论文标题
模块类别，内部双模型和Tambara模块
Module categories, internal bimodules and Tambara modules
论文作者
论文摘要
我们使用tambara模块的理论将模块类别类别的重建定理扩展到非刚性情况。我们显示了单型模块类别的$ 2 $ - 类别$ \ Mathscr {c} $的$ 2 $ - 类别与$ \ Mathscr {c} $的Tambara模块类别中的Algebra的BicateGory与Algebra的BicateGory与BiCateGory之间的双倍关系。使用它，我们证明，可以将环状模块类别重建为$ \ Mathscr {C} $类别中某些免费模块对象的类别，并为其重建性提供足够的条件，以其作为$ \ Mathscr {c} $的模块对象的重建性。为此，我们将Cayley Founctor的定义扩展到非关闭情况，并表明Tambara模块为$ \ Mathscr {C} $ - 模块类别提供了一个proarrow设备，其中$ \ Mathscr {C} $ - 模块函数为$ 1 $ -Morphismss pys a imp aff impaint a impaint a imperaint affime aff impaint。最后，我们表明，所有$ \ Mathscr {C} $ - 模块类别的$ 2 $ - 类别嵌入了$ 2 $ - 类别的类别中，该类别富含在$ \ mathscr {c} $上的tambara模块中，从而通过丰富的操作给出了“'''''结果。
We use the theory of Tambara modules to extend and generalize the reconstruction theorem for module categories over a rigid monoidal category to the non-rigid case. We show a biequivalence between the $2$-category of cyclic module categories over a monoidal category $\mathscr{C}$ and the bicategory of algebra and bimodule objects in the category of Tambara modules on $\mathscr{C}$. Using it, we prove that a cyclic module category can be reconstructed as the category of certain free module objects in the category of Tambara modules on $\mathscr{C}$, and give a sufficient condition for its reconstructability as module objects in $\mathscr{C}$. To that end, we extend the definition of the Cayley functor to the non-closed case, and show that Tambara modules give a proarrow equipment for $\mathscr{C}$-module categories, in which $\mathscr{C}$-module functors are characterized as $1$-morphisms admitting a right adjoint. Finally, we show that the $2$-category of all $\mathscr{C}$-module categories embeds into the $2$-category of categories enriched in Tambara modules on $\mathscr{C}$, giving an ''action via enrichment'' result.
