An (∞,2)-categorical pasting theorem

Hackney, Philip; Ozornova, Viktoriya; Riehl, Emily; Rovelli, Martina

doi:10.1090/tran/8783

An $(\infty ,2)$-categorical pasting theorem
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by Philip Hackney, Viktoriya Ozornova, Emily Riehl and Martina Rovelli;

Trans. Amer. Math. Soc. 376 (2023), 555-597

DOI: https://doi.org/10.1090/tran/8783

Published electronically: October 3, 2022

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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.

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