[Haskell-cafe] N and R are categories, no?

Dominic Steinitz dominic.steinitz at blueyonder.co.uk
Thu Mar 15 17:32:38 EDT 2007

> I haven't formally checked it, but I would bet that this endofunctor
> over N, called Sign, is a monad:

Just to be picky a functor isn't a monad. A monad is a triple consisting of a 
functor and 2 natural transformations which make certain diagrams commute.

If you are looking for examples, I always think that a partially ordered set 
is a good because the objects don't have any elements. A functor is then an 
order preserving map between 2 ordered sets and monad is then a closure 
(http://en.wikipedia.org/wiki/Closure_operator) - I didn't know this latter 
fact until I just looked it up.


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