Long Dimodules and Quasitriangular Weak Hopf Monoids

José Nicanor Alonso Álvarez, José Manuel Fernández Vilaboa and Ramón González Rodríguez
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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

Mathematics, 2021, vol. 9, issue 4, 1-34

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.

Keywords: Braided (symmetric) monoidal category; Long dimodule; (co)quasitriangular weak Hopf monoid (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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