The Kleisli category 
of a monad 
on a category 
has the same objects as 
, while a morphism 
in 
is a morphism 
in 
. The identity on 
is the component 
of the unit.
If 
and 
represent two Kleisli morphisms, their composition is
the morphism
 |
The unit and associativity laws of the monad make this composition associative and give the stated identities. The Kleisli category packages
computations that produce values carrying the effect represented by 
.
