  For a regular multiplier Hopf algebra $A$, the Yetter-Drinfel'd module
category ${}_{A}\mathcal{YD}^{A}$ is equivalent to the centre
$Z({}_{A}\mathcal{M})$ of the unital left $A$-module category
${}_{A}\mathcal{M}$. Then we introduce the generalized $(\alpha,
\beta)$-Yetter-Drinfel'd module categories ${}_{A}\mathcal{GYD}^{A}(\alpha,
\beta)$, which are treated as components of a braided $T$-category. Especially
when $A$ is a coFrobenius Hopf algebra, ${}_{A}\mathcal{YD}^{A}(\alpha, \beta)$
is isomorphic to the unital $\hat{A} \bowtie A(\alpha, \beta)$-module category
${}_{\hat{A} \bowtie A(\alpha, \beta)}\mathcal{M}$. Finally for a
Yetter-Drinfel'd $A$-module algebra $H$, we introduce Yetter-Drinfel'd $(H,
A)$-module category, which is a monoidal.
