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!