论文标题
Grothendieck在黑洞悖论中的观点和复杂性
Grothendieck's point of view and complexity in the black hole paradox
论文作者
论文摘要
这些是关于Grothendieck的观点以及复杂性动力学的观点如何在解释黑洞信息悖论的问题中融合在一起的一些猜测。它们既不完整也不是最终，但似乎是一个新的研究方向。如果阅读，他们可能对一些研究人员有用。基本思想是，仅纠缠无法完全解释黑洞环境中的信息提取。已经提出了复杂性作为替代方案，但仍然是一个模糊的概念。我采用Grothendieck的观点将纠缠熵的概念扩展到一个分类环境中，其中对象（状态）及其地图被考虑在一起，并且地图空间具有附加的拓扑和几何结构，该结构通过sieves，sieves，sheaf和toposes与类别的对象集相结合。
These are some speculations on how Grothendieck's point of view and the idea of complexity dynamics can come together in the problem of explaining the black hole information paradox. They are neither complete, nor final, but can seem like a new direction of research. If read as such they could prove useful to some researchers. The basic idea is that entanglement alone cannot fully account for the information extraction in black hole contexts. Complexity has been proposed as an alternative but remains a vague concept. I employ Grothendieck's point of view to expand the idea of entanglement entropy to a categorical context in which the objects (states) and their maps are considered together and the map space has additional topological and geometric structure that intermingles with the object set of the category via Sieves, Sheafs, and Toposes.
