[Haskell-cafe] Join and it's relation to >>= and return

[Jerzy Karczmarczuk]

Iavor S. Diatchki wrote:

> Ron de Bruijn wrote:
> 
>> I am pretty sure, that >>= is to monads what * is to
>> for example natural numbers, but I don't know what the
>> inverse of >>= is. And I can't really find it anywhere
>> on the web(papers, websites, not a single sole does
>> mention it.  
>>
> this is not quie correct.  (join & return) for a monad are like
> (*,1) or (+,0) for the set of integers.  however those operations on
> integers have more structure than join and return.
> 
> there is no operation for "inverse". in mathematical terms:
> monads are a monoid (given that the notion is generalized considerably
> from its usual use), and not a group. if one was to add such an operation
> (i am not sure what it would do), but it would be of type:
> inverse :: M a -> M a (and of course must satisfy some laws)

I have *nothing* to add, just a question.
Do you /anybody/ know of any edible work on ADJUNCTIONS in the context of
Haskell structures? Perhaps instead of searching for 'inverses' one should
think more about adjoints?...


Jerzy Karczmarczuk