$(\mathrm{\infty },n)$-Limits II: Comparison across models

We show that the notion of $(\mathrm{\infty },n)$-limit defined using the enriched approach and the one defined using the internal approach coincide. We also give explicit constructions of various double $(\mathrm{\infty },n-1)$-categories implementing various join constructions, slice constructions and cone constructions, and study their properties. We further prove that key examples of $(\mathrm{\infty },n)$-categories are (co)complete.