An (\infty ,2) -categorical pasting theorem

An (\infty ,2) -categorical pasting theorem

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...

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Veröffentlicht in:Transactions of the American Mathematical Society 2023-01, Vol.376 (1), p.555-597, Article 555
Hauptverfasser: Hackney, Philip, Ozornova, Viktoriya, Riehl, Emily, Rovelli, Martina
Format: Artikel
Sprache:eng
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Research article
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Zusammenfassung: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8783