$V$-Cat is locally presentable or locally bounded if $V$ is so

G. M. Kelly, Stephen Lack

    Research output: Contribution to journalArticle

    23 Citations (Scopus)


    We show, for a monoidal closed category $V = (V_0,\otimes,I)$, that the category $V$-Cat of small $V $-categories is locally $\lambda$-presentable if $V_0$ is so, and that it is locally $\lambda$-bounded if the closed category $V$ is so, meaning that $V_0$ is locally $\lambda$-bounded and that a side condition involving the monoidal structure is satisfied.

    Original languageEnglish
    Pages (from-to)555-575
    Number of pages21
    JournalTheory and Applications of Categories
    Publication statusPublished - 2001



    • Enriched category
    • Locally bounded category
    • Locally presentable category

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