Embedding n-categories into ($\infty,n$)-categories

While weak versions of n-categories are much more widespread in nature, strict version allows for modelling specific shapes of higher categories. For n=2, we have a complete understanding of their relationship. After introducing the terms and setting up the stage, I will report about this and - time permitting - about work in progress towards analogous results for n>2. This is joint work with Martina Rovelli.