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.