[Haskell-cafe] N and R are categories, no?
nicolas.frisby at gmail.com
Thu Mar 15 19:40:57 EDT 2007
Thanks for keeping me honest ;)
On 3/15/07, Dominic Steinitz <dominic.steinitz at blueyonder.co.uk> wrote:
> > 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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