For a suitable choice of the cube category, we construct a Grothendieck topology on it such that sheaves with respect to this topology are exactly simplicial sets (thus establishing simplicial sets as a reflective subcategory of cubical sets). We then extend the construction of the homotopy coherent nerve to cubical categories and establish an analogue of Lurie's straightening–unstraightening construction.

中文翻译：

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三次调直方法

为了适当地选择多维数据集类别，我们在其上构造了Grothendieck拓扑，以使相对于该拓扑的滑轮完全是单纯集（因此将单纯集建立为立方集的反射子类别）。然后，我们将同态相干神经的构造扩展到立方类别，并建立了Lurie的拉直-拉直结构的类似物。