`CoChoice` is defined in the Haskell profunctors package. If I had to make an unsubstantiated guess, I would say that CoChoice corresponds to cofixpoints/corecursion and CoStrong/ArrowLoop (not shown here but has type `((a, d) ~> (b, d)) -> (a ~> b)`) corresponds to fixpoints/recursion. Like yccs27 was saying, this would mean that cochoice corresponds to apomorphims and costrong corresponds to paramorphisms, though I'm really not sure. `CoStrong` seems to require laziness so it seems like costrong and cochoice should be flipped.