Cosmoi of internal categories

Ross Street*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)


    An internal full subcategory of a cartesian closed category ҩ is shown to give rise to a structure on the 2-category Cat(ҩ), of categories in ҩ which introduces the notion of size into the analysis of categories in ҩ and allows proofs by transcendental arguments. The relationship to the currently popular study of locally internal categories is examined. Internal full subcategories of locally presentable categories (in the sense of Gabriel-Ulmer) are studied in detail. An algorithm is developed for their construction and this is applied to the categories of double categories, triple categories, and so on.

    Original languageEnglish
    Pages (from-to)318
    Number of pages1
    JournalTransactions of the American Mathematical Society
    Issue number2
    Publication statusPublished - 1980


    • Cartesian closed
    • Fibred category
    • Gabriel theory
    • Internal full subcategory
    • Internally complete
    • Locally presentable category
    • Locally small
    • Multiple category
    • Site
    • Sketched structures


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