In the original series of articles by Eilenberg and Mac Lane, they wrote something like:
“Category” has been defined in order to be able to define “functor” and “functor” has been defined in order to be able to define “natural transformation.”
The word “natural” has a long history in mathematics. Category theory is a rigorous interpretation of what it means (neither stronger nor weaker than the more obvious notion of canonical). The first example of a natural transformation is the determinant. What does it mean that it is “natural,” that is compatible across rings of coefficients?
In the original series of articles by Eilenberg and Mac Lane, they wrote something like:
The word “natural” has a long history in mathematics. Category theory is a rigorous interpretation of what it means (neither stronger nor weaker than the more obvious notion of canonical). The first example of a natural transformation is the determinant. What does it mean that it is “natural,” that is compatible across rings of coefficients?