@Anindya

>So the rule is \$$(f', g')\circ (f, g) = (f\circ f', g'\circ g)\$$, ie the first coordinate is the "other way round".

Ahh the composition rule is also backwards. \$$\mathcal{C}^{op}\$$ is trickier than it seems. Thanks a bunch Anindya. I would have gotten lost everywhere in opposite land had I not known this.