Enriched categories as a free cocompletion

Richard Garner, Michael Shulman

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)


    This paper has two objectives. The first is to develop the theory of bicategories enriched in a monoidal bicategory-categorifying the classical theory of categories enriched in a monoidal category-up to a description of the free cocompletion of an enriched bicategory under a class of weighted bicolimits. The second objective is to describe a universal property of the process assigning to a monoidal category V the equipment of V-enriched categories, functors, transformations, and modules; we do so by considering, more generally, the assignation sending an equipment C to the equipment of C-enriched categories, functors, transformations, and modules, and exhibiting this as the free cocompletion of a certain kind of enriched bicategory under a certain class of weighted bicolimits.

    Original languageEnglish
    Pages (from-to)1-94
    Number of pages94
    JournalAdvances in Mathematics
    Publication statusPublished - 5 Feb 2016


    • Enriched bicategory theory
    • Enriched categories
    • Free cocompletions
    • Equipments


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