By the way, I had things backwards here:
> We're taking \\(\mathcal{C}\\) to be the free category on this graph
>
> and \\(\mathcal{D}\\) to be the free category on this bigger graph:
>

I've fixed it. The lecture now reads:
> We're taking \\(\mathcal{D}\\) to be the free category on this graph
>
> and \\(\mathcal{C}\\) to be the free category on this bigger graph:
>