Dan Piponi wrote:
(I got lost somewhere with the levels of quotation there...)
It's more specific than this. Coalgebra, cohomology, codata, comonads and so on derive their name from the fact that they can be described using category theory. In category theory you draw lots of diagrams with arrows in them. When you flip all the arrows round you get a description of something else. Pairs of concepts connected in this way often differ by the prefix "co-". Often theorems you prove about objects have analogous theorems about the respective co-objects. In fact, often the proof is the same, just written with all the arrows pointing the other way.
This carries over to Haskell too. You can sometimes write functional (as in useful) code simply by taking an already existing piece of code and figuring out what flipping the arrows means. It often means something very different, but it still makes sense. A really cool example is the relationship between fold and unfold. But I'll leave that for someone else.
Sounds a lot like the Boolean duality principle. (If a statement works one way, if you flip all the true/false and/or stuff, you get a brand new statement, which also works.)