In this paper we prove that various quasi-categories whose objects are $$\infty $$ ∞ -categories in a very general sense are complete : admitting limits indexed by all simplicial sets. This result and others of a similar flavor follow from a general theorem in which we characterize the data that is required to define a limit cone in a quasi-category constructed as a homotopy coherent nerve. Since all quasi-categories arise this way up to equivalence, this analysis covers the general case. Namely, we show that quasi-categorical limit cones may be modeled at the point-set level by pseudo homotopy limit cones , whose shape is governed by the weight for pseudo limits over a homotopy coherent diagram but with the defining universal property up to equivalence, rather than isomorphism, of mapping spaces. Our applications follow from the fact that the $$(\infty ,1)$$ ( ∞ , 1 ) -categorical core of an $$\infty $$ ∞ -cosmos admits weighted homotopy limits for all flexible weights, which includes in particular the weight for pseudo cones.

中文翻译：

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识别同伦相干神经中的准绝对界限和界限

在本文中，我们证明了对象为非常一般意义上的 $$\infty $$ ∞ -categories 的各种准类别是完备的：允许所有单纯集索引的极限。这个结果和其他类似的结果来自一个一般定理，在这个定理中，我们描述了在构造为同伦相干神经的准类别中定义极限锥所需的数据。由于所有准类别都是以这种方式出现直到等价，因此该分析涵盖了一般情况。即，我们表明准分类极限锥可以在点集级别通过伪同伦极限锥建模，其形状由同伦相干图上的伪极限的权重控制，但具有定义的通用属性直到等价，而不是映射空间的同构。