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arXiv · 2106.03660

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

Philip Hackney·Viktoriya Ozornova·Emily Riehl·Martina Rovelli
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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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Philip Hackney, Viktoriya Ozornova, Emily Riehl, Martina Rovelli. 2021-06-07. An $(\infty,2)$-categorical pasting theorem. https://doi.org/10.1090/tran/8783

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