 |  |
A natural transformation 
is called unital if 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 functors
(indexed with respect to the objects in 
) in question.
