On cyclic star-autonomous categories

J. M. Egger, M. B. McCurdy*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    Abstract

    We discuss . cyclic star-autonomous categories, that is, unbraided star-autonomouscategories in which the left and right duals of every object . p are linked by coherent natural families of isomorphisms. We settle coherence questions which have arisen concerning such cyclicity isomorphisms, and we show that such cyclic structures are the natural setting in which to consider enriched profunctors. Specifically, if . V is a cyclic star-autonomous category, then the collection of . V-enriched profunctors carries a canonical cyclic structure. In the case of braided star-autonomous categories, we discuss the correspondences between cyclic structures and balances or tortile structures. Finally, we show that every cyclic star-autonomous category is equivalent to one in which the cyclicity isomorphisms are identities.

    Original languageEnglish
    Pages (from-to)1706-1725
    Number of pages20
    JournalJournal of Pure and Applied Algebra
    Volume216
    Issue number8-9
    DOIs
    Publication statusPublished - Aug 2012

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