An (∞,2)-categorical pasting theorem

Abstract

We show that any pasting diagram in any(∞,2)(\infty ,2)-category has a homotopically unique composite. This is achieved by showing that the free 2-category generated by a pasting scheme is the homotopy colimit of its cells as an(∞,2)(\infty ,2)-category. We prove this explicitly in the simplicial categories model and then explain how to deduce the model-independent statement from that calculation.