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Applied Categorical Structures

, Volume 11, Issue 3, pp 229–260 | Cite as

Dualizations and Antipodes

  • Brian Day
  • Paddy McCrudden
  • Ross Street
Article

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 Comod f (H) of finite-dimensional representations of H is autonomous is that the Comod f operation is autonomous and so preserves dualization.

monoidal bicategory enriched category bidual antipode quantum group quasi-Hopf algebra braided group comodule 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Brian Day
    • 1
  • Paddy McCrudden
    • 1
  • Ross Street
    • 1
  1. 1.Centre of Australian Category TheoryMacquarie UniversityAustralia

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