Generalized Yetter-Drinfel'd module categories for regular multiplier Hopf algebras

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For a regular multiplier Hopf algebra A, the Yetter-Drinfel'd module category ₐYDᵃ is equivalent to the centre Z(ₐM) of the unital left A-module category ₐM. Then we introduce the generalized (α, β)-Yetter-Drinfel'd module categories ₐGYDᵃ(α, β), which are treated as components of a braided T-category. Especially when A is a coFrobenius Hopf algebra, ₐYDᵃ(α, β) is isomorphic to the unital A A(α, β)-module category A A(α, β)M. Finally for a Yetter-Drinfel'd A-module algebra H, we introduce Yetter-Drinfel'd (H, A)-module category, which is a monoidal.