possible typo: in previous lectures we've defined profunctors as \$$\mathcal{V}\$$-enriched functors \$$\mathcal{X}^\text{op}\times\mathcal{Y}\rightarrow\mathcal{V}\$$ but here we're using \$$\mathcal{X}\times\mathcal{Y}^\text{op}\rightarrow\mathcal{V}\$$ – is this a mistake or are we swapping round for a reason?