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
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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