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

Abstract

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

45 pages; comments welcome