As Eilenberg-Mac Lane first observed, “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”.
Saunders Mac Lane, Categories for the Working Mathematician
He’s saying that he made up categories and functors because what he really wanted to study was the idea of natural transformations, and the former notions are needed to define the latter. Or: categories and functors are nice, but natural transformations are the bomb.
Saunders Mac Lane, Categories for the Working Mathematician
Is there a way to explain that to a non-mathematician?
He’s saying that he made up categories and functors because what he really wanted to study was the idea of natural transformations, and the former notions are needed to define the latter. Or: categories and functors are nice, but natural transformations are the bomb.
Or even a non-category theorist?