How strict is strictification?

Alexander Campbell

    Research output: Contribution to journalArticlepeer-review


    The subject of this paper is the higher structure of the strictification adjunction, which relates the two fundamental bases of three-dimensional category theory: the Gray-category of 2-categories and the tricategory of bicategories. We show that – far from requiring the full weakness provided by the definitions of tricategory theory – this adjunction can be strictly enriched over the symmetric closed multicategory of bicategories defined by Verity. Moreover, we show that this adjunction underlies an adjunction of bicategory-enriched symmetric multicategories. An appendix introduces the symmetric closed multicategory of pseudo double categories, into which Verity's symmetric multicategory of bicategories embeds fully.
    Original languageEnglish
    Pages (from-to)2948-2976
    Number of pages29
    JournalJournal of Pure and Applied Algebra
    Issue number7
    Publication statusPublished - Jul 2019


    • strictification
    • bicategory
    • 2-category
    • adjunction
    • multicategory
    • double category
    • Gray-category
    • bicategory-enriched
    • three-dimensional category theory


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