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A unital natural transformation is a natural transformation 
such that the
leftmost diagram above commutes. Similarly,
a natural transformation 
is called unital if the diagram on the right-hand
side above commutes.
Note that in these definitions, 
, 
, and 
are all objects in a tensor
category 
, 
is the neutral (or identity) object
in 
,
and the juxtaposition 
is shorthand for the tensor product 
in 
. What's more, the subscripts attached to the transformations
and 
denote the components of the natural transformations
(indexed with respect to the objects in 
) in question.
