|
|
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.