A couple minor corrections on the lecture notes:

> How can we define
>
> $\Phi \otimes \Psi \colon X \otimes X' \nrightarrow Y \otimes Y' ?$

should probably use \mathcal to denote the \$$\mathcal{V}\$$-categories.

> we define
>
> $(\mathcal{X} \times \mathcal{Y})((x,y), \, (x',y')) = \mathcal{X}(x,x') \otimes \mathcal{Y}(y,y') .$

should probably use the \$$\otimes\$$ symbol on the left to denote tensoring.