@John Yes, now that I have understood this, I totally see why modern theorists want to define only one type of functor. I just got confused by the mentioning of "contravariant" here and there (especially when we were trying to understand the op-trick under [Lecture 47](https://forum.azimuthproject.org/discussion/2253/lecture-47-chapter-3-adjoint-functors/p1)) and the lack of really explicit formulation (e.g. what exactly is the contravariant thing? what does "contravariant" mean when contravariant functors are already obsolete?), precisely because of what you nicely explained in [#28](https://forum.azimuthproject.org/discussion/comment/19895/#Comment_19895), i.e. when we use the op-trick we should _not_ really still keep talking about "contravariant"!
For someone (aka me) who does not (yet) know enough category theory to properly reason about such things as notational/methodological conventions, this kind of apparently pedantic details can easily become unnecessary hurdles, but once they are clarified, the picture suddenly becomes a lot clearer. :)