Not really. The big important part of monads is flattening/unnesting the output. Basically, if you can convert a `Foo<T>` into a `Foo<U>` by applying a functio

Not really. The big important part of monads is flattening/unnesting the output. Basically, if you can convert a `Foo<T>` into a `Foo<U>` by applying a function `T -> U`, it's a monoid. Think `map` or `fold`. But if you can convert a `Foo<T>` into a `Foo<U>` by applying a function `T -> Foo<U>`, it's a monad. Flattening is "some logic", but not any logic, it's inherent to `Foo<>` itself.