宇宙学中commony的Tannaka对偶
Tannaka duality for comonoids in cosmoi
摘要：
Tannaka对偶的一个经典结果是，域上的余代数可以从其有限维表示的范畴通过使用将表示发送到其底层向量空间的遗忘函子来重构。给出了一个相应的识别结果，刻画了那些具有有限维向量空间函子的范畴，它们等价于余代数的有限维表示范畴.本文将这些问题推广到任意宇宙，即完备和余完备的对称monoidal闭范畴。而不是表示对有限维向量空间，我们期待在表示对象的宇宙有一个对偶。我们给出了一个充要条件，确保一个commonly可以重建从其表示，我们的特点类别的表示某些commonly。我们将这一结果应用到某些类别的过滤模块，用于研究p-adic伽罗瓦表示。
英文摘要：
A classical result of Tannaka duality is the fact that a coalgebra over a field can be reconstructed from its category of finite dimensional representations by using the forgetful functor which sends a representation to its underlying vector space. There is also a corresponding recognition result, which characterizes those categories equipped with a functor to finite dimensional vector spaces which are equivalent to the category of finite dimensional representations of a coalgebra. In this paper we study a generalization of these questions to an arbitrary cosmos, that is, a complete and cocomplete symmetric monoidal closed category. Instead of representations on finite dimensional vector spaces we look at representations on objects of the cosmos which have a dual. We give a necessary and sufficient condition that ensures that a comonoid can be reconstructed from its representations, and we characterize categories of representations of certain comonoids. We apply this result to certain categories of filtered modules which are used to study p-adic Galois representations.
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