We introduce the notion of weighted limit in an arbitrary quasi-category, suitably generalizing ordinary limits in a quasi-category, and classical weighted limits in an ordinary category. This is accomplished by generalizing Joyal’s approach: we identify a meaningful construction for the quasi-category of weighted cones over a diagram in a quasi-category, whose terminal object is the weighted limit of the considered diagram. We then show that each weighted limit can be expressed as an ordinary limit. When the quasi-category arises as the homotopy coherent nerve of a category enriched over Kan complexes, we generalize an argument by Riehl-Verity to show that the weighted limit agrees with the homotopy weighted limit in the sense of enriched category theory, for which explicit constructions are available. When the quasi-category is complete, tensored and cotensored over the quasi-category of spaces, we discuss a possible comparison of our definition of weighted limit with the approach by Gepner-Haugseng-Nikolaus.

我们在任意准类别中引入加权极限的概念，在一般类别中适当地推广普通极限，而在普通类别中引入经典加权极限。这是通过概括Joyal的方法来完成的：我们在拟类别中的图上确定加权锥的拟类别的有意义的构造，该类的最终对象是所考虑图的加权极限。然后，我们证明每个加权极限可以表示为普通极限。当准类别作为富集在Kan络合物上的类别的同伦同调相干神经出现时，我们概括了Riehl-Verity的论点，以证明加权极限与富集类别理论意义上的同伦加权极限一致，对此，显式结构是可利用的。准类别完成后，