The paper is concerned with endomorphism algebras for weak Doi-Hopf modules. Under the condition “weak Hopf-Galois extensions”,
we present the structure theorem of endomorphism algebras for weak Doi-Hopf modules, which extends Theorem 3.2 given by Schneider
in . As applications of the structure theorem, we obtain the Kreimer-Takeuchi theorem (see Theorem 1.7 in ) and the
Nikshych duality theorem (see Theorem 3.3 in ) in the case of weak Hopf algebras, respectively.