$(\infty ,n)$-Limits I: Definition and first consistency results

Abstract

We give a model-independent definition of limits for diagrams valued in an $(\infty ,n)$-category. We show that this definition is compatible with the existing notion of homotopy 2-limits for 2-categories, with the existing notion of $(\infty ,1)$-limits for $(\infty ,1)$-categories, and with itself across different values of $n$.

31 pages; v2+v3 are model-independent versions of v1; v3 is the final version to appear in Canadian Journal of Mathematics