 |  |
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.
