As is usual, let's say an (n, k)-category is something with objects, morphisms, 2-morphisms, ..., n-morphisms, such that all j-morphisms for j > k are invertible, everything meant in the weak sense. ...
The following question can be thought as a sequel of this one. Here I'm looking for a big list of example of weak algebraic structures: here weak means that the structure (i.e. operations) need not ...
Of course, personally, I think the answer is a big Yes! However once, a while ago, while giving a talk about higher category theory, I was asked a question about whether higher category theory was ...