ABSTRACT
When we say that we want to find “models” for (∞, n)-categories, we are looking for concrete mathematical objects that encode this desired structure. But first, we need to answer a more basic question: What is an (∞, n)-category anyway? A short answer is that it is should be a higher category that is given up to homotopy, in some sense. Alternatively, it is a higher category in which sufficiently high-level morphisms are invertible.
