Abstract We prove a uniqueness type theorem for (weak, total) integrals on a Frobenius cowreath in a monoidal category. When the cowreath is, moreover, pre-Galois, we construct a Morita context relating the subalgebra of coinvariants and a certain wreath algebra. Then we see that the strictness of the Morita context is related to the Galois property of the cowreath and the existence of a weak total integral on it. We apply our results to quasi-Hopf algebras.

中文翻译：

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Frobenius 花环和 Morita 背景

摘要 我们证明了幺半群中 Frobenius 环上的（弱，全）积分的唯一性类型定理。此外，当 coreath 是 pre-Galois 时，我们构建了一个 Morita 上下文，该上下文将 coinvariants 的子代数和某个花环代数相关联。然后我们看到 Morita 上下文的严格性与 cowreath 的 Galois 性质和其上存在弱全积分有关。我们将我们的结果应用于准 Hopf 代数。