Is "cofunctor" an accepted term for contravariant functors?
Solution 1:
I might be wrong, but I don't think it is completely right to call a controvariant functor "cofunctor" (at least if we want to stick to the convention of using the particle co- to mean and evoke duality) because the sentence "$T$ is a functor" is clearly self-dual, as Mac-Lane explicitely pointed out in his Categories for the Working Mathematician. So, given a functor $T$ a "cofunctor", interpreted as the dual concept, would be just $T$ itself.