The Catalan simplicial set II

Mitchell Buckley*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)


    The Catalan simplicial set ℂ is known to classify skew-monoidal categories in the sense that a map from ℂ to a suitably defined nerve of Cat is precisely a skew-monoidal category (Buckley et al. 2014). We extend this result to the case of skew monoidales internal to any monoidal bicategory B. We then show that monoidal bicategories themselves are classified by maps from ℂ to a suitably defined nerve of Bicat and extend this result to obtain a definition of skew-monoidal bicategory that aligns with existing theory.

    Original languageEnglish
    Pages (from-to)765-796
    Number of pages32
    JournalApplied Categorical Structures
    Issue number6
    Publication statusPublished - 1 Dec 2016


    • Bicategory
    • Catalan
    • Category
    • Monoidal
    • Nerve
    • Simplicial set
    • Skew monoidal


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