Dualizations and antipodes

Brian Day*, Paddy McCrudden, Ross Street

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    20 Citations (Scopus)

    Abstract

    Because an exact pairing between an object and its dual is extraordinarily natural in the object, ideas of R. Street apply to yield a definition of dualization for a pseudomonoid in any autonomous monoidal bicategory as base; this is an improvement on Day and Street, Adv. in Math. 129 (1997), Definition 11, p. 114. We analyse the dualization notion in depth. An example is the concept of autonomous (which, usually in the presence of a symmetry, also has been called "rigid" or "compact") monoidal category. The antipode of a quasi-Hopf algebra H in the sense of Drinfeld is another example obtained using a different base monoidal bicategory. We define right autonomous monoidal functors and their higher-dimensional analogue. Our explanation of why the category Comodf (H) of finite-dimensional representations of H is autonomous is that the Comodf operation is autonomous and so preserves dualization.

    Original languageEnglish
    Pages (from-to)229-260
    Number of pages32
    JournalApplied Categorical Structures
    Volume11
    Issue number3
    DOIs
    Publication statusPublished - Jun 2003

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