Coherence for tricategories

R. Gordon, A. J. Power, Ross Street

    Research output: Book/ReportBookpeer-review

    Abstract

    This work defines the concept of tricategory as the natural 3-dimensional generalization of bicategory. Trihomomorphism and triequivalence for tricategories are also defined so as to extend the concepts of homomorphism and biequivalence for bicategories. The main theorem is a coherence theorem for tricategories which asserts the existence of a triequivalence between each tricategory and some V-category, where V is the category of 2-categories equipped with the strong tenser product of J. W. Gray. Further, it is shown that while not every tricategory is triequivalent to a 3-category, every tricategory that is locally a 2-category and whose composition is a 2-functor is triequivalent to a 3-category. The work has applications to cohomology theory, homotopy theory, bicategory enriched categories, and bicategories with extra structure.

    Original languageEnglish
    Place of PublicationProvidence, RI
    PublisherAmerican Mathematical Society
    Number of pages81
    Volume117
    Edition558
    ISBN (Print)9780821803448, 1470401371
    DOIs
    Publication statusPublished - Sep 1995

    Keywords

    • TRICATEGORY
    • MONOIDAL BICATEGORY
    • GRAY-CATEGORY
    • ALGEBRAIC HOMOTOPY 3-TYPE
    • LAX FUNCTOR OF TRICATEGORIES
    • TRIHOMOMORPHISM
    • TRIEQUIVALENCE
    • CUBICAL FUNCTOR
    • CUBICAL TRICATEGORY
    • PREREPRESENTATION
    • BICATEGORIES
    • CATEGORIES

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