Okay, you actually are suggesting that:

> This amount to replacing the \\(\mathcal{V}(x, y)\otimes\mathcal{V}(y, z)\leq\mathcal{V}(x, z)\\) condition with \\(\mathcal{V}(y, z)\otimes\mathcal{V}(x, y)\leq\mathcal{V}(x, z)\\) – similarly to how we define \\(\text{hom}\\) in a \\(\textbf{Set}\\)-category. Then the proof would go through.

Sorry, I'm not always good at reading what people write!