Abstract: In the world of $(\infty,1)$-categories, it is well-known that the composition of specified morphisms is well-defined up to a contractible choice. The situation for $(\infty,2)$-categories is more subtle, as there are many potential ways of composing 2-cells. In a joint work in progress with Hackney, Riehl, Rovelli, we prove a uniqueness statement for the composition of so-called pasting diagrams, which I will explain during the talk.