Weighted limits in an $$(\infty ,1)$$-category

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