Two-dimensional regularity and exactness

John Bourke, Richard Garner*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    We define notions of regularity and (Barr-)exactness for 2-categories. In fact, we define three notions of regularity and exactness, each based on one of the three canonical ways of factorising a functor in Cat: as (surjective on objects, injective on objects and fully faithful), as (bijective on objects, fully faithful), and as (bijective on objects and full, faithful). The correctness of our notions is justified using the theory of lex colimits [12] introduced by Lack and the second author. Along the way, we develop an abstract theory of regularity and exactness relative to a kernel-quotient factorisation, extending earlier work of Street and others [24,3].

    Original languageEnglish
    Pages (from-to)1346-1371
    Number of pages26
    JournalJournal of Pure and Applied Algebra
    Volume218
    Issue number7
    DOIs
    Publication statusPublished - Jul 2014

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