2-nerves for bicategories

Stephen Lack*, Simona Paoli

*Corresponding author for this work

    Research output: Contribution to journalArticle

    29 Citations (Scopus)

    Abstract

    We describe a Cat-valued nerve of bicategories, which associates to every bicategory a simplicial object in Cat, called the 2-nerve. This becomes the object part of a 2-functor N : NHom → [Δop,Cat], where NHom is a 2-category whose objects are bicategories and whose 1-cells are normal homomorphisms of bicategories. The 2-functor N is fully faithful and has a left biadjoint, and we characterize its image. The 2-nerve of a bicategory is always a weak 2-category in the sense of Tamsamani, and we show that NHom is biequivalent to a certain 2-category whose objects are Tamsamani weak 2-categories.

    Original languageEnglish
    Pages (from-to)153-175
    Number of pages23
    JournalK-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences
    Volume38
    Issue number2
    DOIs
    Publication statusPublished - Jan 2008

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