I wrote:

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

Michael wrote:

> According to the definition above, \\(x,y \in \mathrm{Ob}(\mathcal{X})\\).

Right.

> But in order for \\(\mathcal{X}(x,y)\\) to be an element of \\(\mathcal{V}\\), \\(x,y \in V\\) must be true also?

No. I didn't say that.

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

Michael wrote:

> According to the definition above, \\(x,y \in \mathrm{Ob}(\mathcal{X})\\).

Right.

> But in order for \\(\mathcal{X}(x,y)\\) to be an element of \\(\mathcal{V}\\), \\(x,y \in V\\) must be true also?

No. I didn't say that.