Abstract: Let k be a field, and(H,α)a monoidal Hom-Hopf algebra with bijective antipode. If(H,α)is commutative, noetherian, semisimple and cosemisimple, then the category _HHYD ^H of Hom-Yetter-Drinfeld modules is semisimple. That is Let(H,α)be commutative. Assume that HHYD ^H satisfies some condition, and that the functor(-)^coH:_HHYD ^H→H(M_k)is exact. If (M,μ)∈_HHYD ^H is finitely generated as an(H,α)-module, then (M,μ) is a projective object in HHYD ^H.

Key words: noetherian, Hom-Yetter-Drinfeld modules, semisimple, commutation, monoidal Hom-Hopf algebras