Definition of restriction of relation

Question

let be $\mathcal{R}$ a binary relation on $X$, and $\mathcal{T}$ a binary relation on $Y$, $\mathcal{T}$ is restriction of $\mathcal{R}$ if:

1) $Y \subseteq X$

2) $\forall a,b \in Y( a T b \leftrightarrow a R b)$

Is correct?

Thanks in advance!