Re: [Haskell-cafe] From monads to monoids in a small category

On Tue, Sep 4, 2012 at 3:39 AM, Alberto G. Corona wrote:

"Monads are monoids in the category of endofunctors"

This Monoid instance for the endofunctors of the set of all elements of (m a) typematch in Haskell with FlexibleInstances:

instance Monad m => Monoid (a -> m a) where mappend = (>=>) -- kleisly operator mempty = return

The objects of a Kliesli category for a monad m aren't endofunctors. You want something like: instance Monad m => Monoid (m a -> m (m a)) where ... /These/ are endofunctors, in virtue of join transforming an m (m a) into an (m a).