Right on, Jean!

It's funny, but exactly that question of terminology (prone, supine, etc) came up a few weeks ago in some joint work with a student here. I made the same case to him, almost exactly, that Jean Benabou just made. And one other objection: I'd like category theory no longer to be regarded as nonsense in this country --- it still is in many quarters, as I could easily prove --- and such terminology is not exactly helpful to the cause! Peter May ps: Then again, I don't much like using the overused words cartesian and cocartesian.