I am a bit confused on the notation.

>1. one specifies a set \\(\mathrm{Ob}(\mathcal{X})\\), elements of which are called **objects**;

>2. for every two objects \\(x,y\\), one specifies an element \\(\mathcal{X}(x,y)\\) of \\(\mathcal{V}\\).

According to the definition above, \\(x,y \in \mathrm{Ob}(\mathcal{X})\\). But in order for \\(\mathcal{X}(x,y)\\) to be an element of \\(\mathcal{V}\\), \\(x,y \in V\\) must be true also? Then what is the difference between \\(\mathrm{Ob}(\mathcal{X})\\) and \\(V\\)?

>1. one specifies a set \\(\mathrm{Ob}(\mathcal{X})\\), elements of which are called **objects**;

>2. for every two objects \\(x,y\\), one specifies an element \\(\mathcal{X}(x,y)\\) of \\(\mathcal{V}\\).

According to the definition above, \\(x,y \in \mathrm{Ob}(\mathcal{X})\\). But in order for \\(\mathcal{X}(x,y)\\) to be an element of \\(\mathcal{V}\\), \\(x,y \in V\\) must be true also? Then what is the difference between \\(\mathrm{Ob}(\mathcal{X})\\) and \\(V\\)?