等变范畴的 Mackey 化 I
Mackeyfication of equivariant categories I
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中文总结 AI 辅助
研究通过 Mackey 2 - 函子构造等变范畴的逼近，包括左右两边的 Mackey 化，受 Boltje 工作启发，通过标记变换关联左右 Mackey 化，并给出了相关例子。
中文摘要 AI 辅助
通俗来讲，‘等变范畴’指的是一族加法范畴$\mathcal{A}(G)$，它通过一个 2 - 函子依赖于有限群$G$。我们通过 Mackey 2 - 函子在左右两边构造等变范畴的逼近。其思路是以最小方式扩大$\mathcal{A}$以使归纳出现。这些‘Mackey 化’受 Boltje 关于普通 Mackey 1 - 函子工作的启发。我们还通过一个标记变换关联左右 Mackey 化。最后讨论了例子。
英文摘要
Colloquially speaking, `equivariant categories' refer to families of additive categories $\mathcal{A}(G)$ depending 2-functorially on a finite group $G$. We construct approximations of equivariant categories by Mackey 2-functors, both on the left and on the right. The idea is to enlarge $\mathcal{A}$ in a minimal way to make induction appear. These `mackeyfications' are inspired by Boltje's work with ordinary Mackey 1-functors. We also relate our left and right mackeyfications via a mark transformation. Finally we discuss examples.
