论文标题
$ \ infty $ - 类别
A monoidal Grothendieck construction for $\infty$-categories
论文作者
论文摘要
我们构建了Lurie联合国/拉直等价的单一版本。更详细地，对于任何对称的单体$ \ infty $-类$ \ mathbf c $，我们赋予了$ \ infty $ - 在$ \ mathbf c $上的$ \ infty $ - 具有（自然定义的）符号单体结构，并证明它是$ $ y $ $ cy $ - C $至$ \ Mathbf {Cat} _ \ infty $。 实际上，我们通过对此陈述进行分类，从任何$ \ infty $ - operad上做到这一点，从而证明了对函子的更强有力的陈述，该函数分配给了$ \ infty $ -Category $ \ mathbf c $它的cocartesian纤维类别，其一方面是$ \ m athbf cat cat Inftty $ nftty $ formant ost $ \ mathbf forment of $ \ mathbf {_________________________________ nhand of the the the \ in thefty infty y Inf the the the thefty。
We construct a monoidal version of Lurie's un/straightening equivalence. In more detail, for any symmetric monoidal $\infty$-category $\mathbf C$, we endow the $\infty$-category of coCartesian fibrations over $\mathbf C$ with a (naturally defined) symmetric monoidal structure, and prove that it is equivalent the Day convolution monoidal structure on the $\infty$-category of functors from $\mathbf C$ to $\mathbf{Cat}_\infty$. In fact, we do this over any $\infty$-operad by categorifying this statement and thereby proving a stronger statement about the functors that assign to an $\infty$-category $\mathbf C$ its category of coCartesian fibrations on the one hand, and its category of functors to $\mathbf{Cat}_\infty$ on the other hand.
