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Generalization of a modular functor

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1765)

Abstract

In this chapter we are defining enhanced double categories \( \widetilde{Cob}^ \cap \) which are equivalent to Cob but have larger sets of 1-arrows. These 1-arrows, called arc-diagrams, encode the structure of certain coends. The reason to introduce them is to define horizontal compositions that do not require braidings. Hence, it will be also be possible to define a TQFT functor with only canonical isomorphisms. The construction is described in Section 7.3. It requires a modification of the double category of tangles to reflect the modifications in the enhanced cobordism-category.

We describe how the braided Hopf algebra F and its integrals look like in familiar examples. Specifically, we consider the case of a semisimple monoidal category as well as the example of the category of modules of a linear ribbon Hopf algebras in the original sense.

Keywords

  • Hopf Algebra
  • Simple Object
  • Monoidal Category
  • Canonical Isomorphism
  • Grouplike Element

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). Generalization of a modular functor. In: Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners. Lecture Notes in Mathematics, vol 1765. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44625-7_8

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  • DOI: https://doi.org/10.1007/3-540-44625-7_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42416-1

  • Online ISBN: 978-3-540-44625-5

  • eBook Packages: Springer Book Archive