John, You write:
Yes, you are describing 'co-monads'.
Good catch, but actually, that's too weak. i'm requesting something that is
both a monad and a co-monad. That makes it something like a bi-algebra, or a
Hopf algebra. This, however, is not the full story. i'm looking for a
reference to the full story. Surely, someone has already developed this
theory.
Best wishes,
--greg
From: John Meacham
Now, are there references for a theory of monads and take-out options? For example, it seems that all sensible notions of containers have take-out. Can we make the leap and define a container as a monad with a notion of take-out? Has this been done? Are there reasons for not doing? Can we say what conditions are necessary to ensure a notion of take-out?
Yes, you are describing 'co-monads'. here is an example that a quick web search brought up, and there was a paper on them and their properties published a while ago http://www.eyrie.org/~zednenem/2004/hsce/Control.Comonad.html the duals in that version are extract - return duplicate - join extend - flip (>>=) (more or less) John -- John Meacham - ⑆repetae.net⑆john⑈ -- L.G. Meredith Managing Partner Biosimilarity LLC 806 55th St NE Seattle, WA 98105 +1 206.650.3740 http://biosimilarity.blogspot.com