@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.