I'm looking to understand the conceptual process that brought Eilenberg and Mac Lane in developing the basic concepts of category theory.
I quote Mac Lane's book "Category theory for working mathematicians":
"...An adequate treatment of the natural isomorphisms occurring for such limits was a major motivation of the first Eilenberg-Mac Lane paper on category theory [The general theory of natural equivalence]..."
Here's my question:
What are these natural isomorphisms that Mac Lane were referring to?