People are used to the prefix co- flipping arrows in a concept1, and I have seen people using cofunctor to mean a functor that flips arrows, i.e. that takes $A \to B$ to $FB \to FA$. I know this concept by the name contravariant functor, which I believe is standard, and contrasted with a covariant functor which doesn't flip arrows – the latter making the name cofunctor particularly unhelpful.
Nevertheless, Wiktionary and Wikipedia (last sentence in the contravariance paragraph) both back up this usage, though uncitedly, so it seems to have some traction. Is there any substance to this usage? Are there any authors who support it, or mention it?
If it is just incorrect, has anyone authoritative dismissed it in a citeable way, such that it could be banished from Wikipedia in future?
Edit: I've also heard contrafunctor used to mean a contravariant functor. Does this mean there are people who use cofunctor to mean covariant functor?
1 What do I mean by "concept" here? Well, an ncept with the arrows flipped, of course.