  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. When the quasi-category arises as
the homotopy coherent nerve of a category enriched over Kan complexes, we use
techniques 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.
