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

[Steve Downey]

Picky is good, because it helps me realize things like I haven't been
paying enough attention to unit and join. Other than realizing that
they make the box diagram and triangle diagram commute.

-smd

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.
>
> Dominic.
>
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