Nerve for 2-dimensional categories

2-dimensional categories are higher versions of ordinary categories and allow for more structure. In particular, they help formalize results in mathematical physics or derived algebraic geometry, such as the cobordism hypothesis or six functor formalism. In this talk, I will define 2-dimensional categories – 2-categories, double categories, (∞,2)-categories, and double ∞-categories – and provide motivating examples. I will then explain how these 2-dimensional structures relate to each other.