A braided T-category over weak monoidal Hom-Hopf algebras.

In this paper, we define and study weak monoidal Hom-Hopf algebras, which generalize both weak Hopf algebras and monoidal Hom-Hopf algebras. Let H be a weak monoidal Hom-Hopf algebra with bijective antipode and let Aut w m H H (H) be the set of all automorphisms of H , we introduce a category H 𝒲 ℳ ℋ 𝒴 𝒟 H (α , β) with α , β ∈ Aut w m H H (H) and construct a braided T -category 𝒲 ℳ ℋ 𝒴 𝒟 (H) having all the categories H 𝒲 ℳ ℋ 𝒴 𝒟 H (α , β) as components. [ABSTRACT FROM AUTHOR]