An algebraic definition of (∞,n)-categories

Camell Kachour

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    In this paper we define a sequence of monads T(∞, n)(n ε N) on the category ∞-Gr of ∞-graphs. We conjecture that algebras for T(∞, 0), which are defined in a purely algebraic setting, are models of ∞-groupoids. More generally, we conjecture that T(∞;n)-algebras are models for (∞, n)-categories. We prove that our (∞, 0)-categories are bigroupoids when truncated at level 2.
    Original languageEnglish
    Pages (from-to)775-807
    Number of pages33
    JournalTheory and Applications of Categories
    Publication statusPublished - 2015


    • (∞n)-categories
    • Homotopy types
    • Weak ∞-groupoids


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