Editing Monad (functional programming) (section)

=== Collections ===
Any collection with a proper {{mvar|append}} is already a monoid, but it turns out that <code>List</code> is not the only [[Collection (abstract data type)|collection]] that also has a well-defined {{mvar|join}} and qualifies as a monad.
One can even mutate <code>List</code> into these other monadic collections by simply imposing special properties on {{mvar|append}}:{{efn|Category theory views these collection monads as adjunctions between the [[free functor]] and different functors from the [[category of sets]] to the [[category of monoids]].}}{{efn|name= monoid|1= Here the task for the programmer is to construct an appropriate monoid, or perhaps to choose a monoid from a library.}}
{| class="wikitable"
|-
! rowspan=2 | Collection !! colspan=3 | Monoid properties !! colspan=2 | Combinatoric properties
|-
! Commutative? !! Idempotent? !! Details !! Ordered? !! Unique items?
|-
| List || {{No}} || {{No}} || [[Free monoid]] || {{Yes}} || {{No}}
|-
| Finite [[multiset]] || {{Yes}} || {{No}} || || {{No}} || {{No}}
|-
| Finite [[set (mathematics)|set]] || {{Yes}} || {{Yes}} || || {{No}} || {{Yes}}
|}