When explaining monads to beginners (having an imperative background), I found myself to say that there is <i>roughly</i> three &quot;groups&quot; of monads (because they&#39;re always worried about their cost, i.e. their incidental complexity):<br>

<br>- Function-oriented monads (e.g. State, Reader, Cont)<br>- Reductible data-oriented monads (e.g. Maybe, Identity, Writer)<br>- Irreductible data-oriented monads (e.g. List, free monads) (which, as I understood, have a (&gt;&gt;=) operation that has a quadratic complexity if not used properly)<br>

<br>Are there others &quot;groups&quot; I&#39;m missing and is there terms to formalize them?<br>