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Long Dimodules and Quasitriangular Weak Hopf Monoids

Author

Listed:
  • José Nicanor Alonso Álvarez

    (Departamento de Matemáticas, Universidade de Vigo, Campus Universitario Lagoas-Marcosende, E-36280 Vigo, Spain)

  • José Manuel Fernández Vilaboa

    (Departamento de Álxebra, Universidade de Santiago de Compostela, E-15771 Santiago de Compostela, Spain)

  • Ramón González Rodríguez

    (Departamento de Matemática Aplicada II, Universidade de Vigo, Campus Universitario Lagoas Marcosende, E-36310 Vigo, Spain)

Abstract

In this paper, we prove that for any pair of weak Hopf monoids H and B in a symmetric monoidal category where every idempotent morphism splits, the category of H - B -Long dimodules H B Long is monoidal. Moreover, if H is quasitriangular and B coquasitriangular, we also prove that H B Long is braided. As a consequence of this result, we obtain that if H is triangular and B cotriangular, H B Long is an example of a symmetric monoidal category.

Suggested Citation

  • José Nicanor Alonso Álvarez & José Manuel Fernández Vilaboa & Ramón González Rodríguez, 2021. "Long Dimodules and Quasitriangular Weak Hopf Monoids," Mathematics, MDPI, vol. 9(4), pages 1-34, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:424-:d:503075
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