A natural transformation 
from 
to 
, for functors 
between categories 
and 
, consists of a family 
of morphisms
in 
which are indexed by the objects 
of 
so that, for each morphism 
between objects in 
, the equality
 |
holds. The elements 
are called the components of the natural transformation.
If all the components 
are isomorphisms in 
,
then 
is called a natural isomorphism between 
and 
.
In this case, one writes 
.
