We give a definition of the Gray tensor product in the setting of scaled simplicial sets which is associative and forms a left Quillen bifunctor with respect to the bicategorical model category of Lurie. We then introduce a notion of oplax functor in this setting, and use it in order to characterize the Gray tensor product by means of a universal property. A similar characterization was used by Gaitsgory and Rozenblyum in their definition of the Gray product, thus giving a promising lead for comparing the two settings.

中文翻译：

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(∞,2)-范畴的灰色张量积和松散函子

我们在标度单纯集的设置中给出了灰色张量积的定义，它是关联的，并形成关于 Lurie 的双分类模型类别的左 Quillen 双函子。然后，我们在此设置中引入了 oplax 函子的概念，并使用它来通过通用属性来表征灰色张量积。Gaitsgory 和 Rozenblyum 在他们对 Gray 产品的定义中使用了类似的特征，从而为比较两种设置提供了有希望的线索。