> A monoid is anything with an associative append and an identity operation.
It doesn't have to be an append, it can be any associative operation that is closed over its domain and the domain features an identitiy element.
> A monad is a form of monoid (in the category of endofunctors; what's the problem?),
A category theoretic monad may be a "monoid in the category of endofunctors". The Monad type is not, strictly speaking, a monoid (but looks like one if you squint a little).
> but monoids are not necessarily monads.
Who said they are? :)
