An $(\infty ,2)$-categorical pasting theorem

Abstract

We show that any pasting diagram in any $(\infty ,2)$-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 $(\infty ,2)$-category. We prove this explicitly in the simplicial categories model and then explain how to deduce the model-independent statement from that calculation.

42 pages, comments welcome; v2: new section on related work with updated references; v3: moved the analysis of pushouts of Dwyer maps to arXiv:2205.02353 in order to prove a more general version of the result than is needed here; v4: final version

References in corpus (1)

• The Gray tensor product for 2-quasi-categories

Cited by in corpus (2)

• Pushouts of Dwyer maps are $(\infty ,1)$-categorical
• Nerves and cones of free loop-free ω-categories