中文摘要：

通过引入Yetter-Drinfeld模范畴中弱Hopf代数和弱相对Hopf模的概念,得到Yetter-Drinfeld模范畴中弱相对Hopf模的基本定理：设L是具有双射对极的Hopf代数,H是范畴LLYD中的弱Hopf代数,A是范畴LLYD中的弱右H-余模代数,如果在范畴LLYD中存在一个右H-余模映射φ：H→A并且是代数同态,M是范畴LLYD中的一个弱右（H,A）-相对Hopf模,则映射F：Mco HAco HA→M,F（ma）=m.a是一个弱（H,A）-相对Hopf模同构.

英文摘要：

With the help of the definitions of weak Hopf algebra and weak relative Hopf module in Yetter-Drinfeld module categories,the fundamental theorem for weak relative Hopf modules in Yetter-Drinfeld module categories was obtained.Let L be a Hopf algebra together with a bijective antipode and H be a weak Hopf algebra in category LLYD,then if there exists a right H-comodule map φ：H→A in LLYD which is also an algebra map,M is a weak（H,A）-relative Hopf module in LLYD,thus the mapF：Mco HAco HA→M,F（ma）=m·ais an isomorphism of weak（H,A）-relative Hopf modules.