Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
You could look at the original paper. There you'll find an extensive discussion and many applications to group theory and topology. – t.b. Nov 23 '11 at 9:23
@t.b.: thanks. I've already read that paper but it doesn't explacoverin the path that guided the authors to the creations of those categorical concepts, that is the mathematical philosophy behind category theory. – Giorgio Mossa Nov 23 '11 at 10:08
Okay, I see. Then I think you could do worse than look at Chapter 2 of Krömer's Tool and Object: A History and Philosophy of Category Theory, here's the table of contents of that chapter: part 1, part 2 and here's an extensive review by Corry of the entire book. – t.b. Nov 23 '11 at 10:52
"I didn't invent categories to study functors; I invented them to study natural transformations." - Mac Lane Just some context. – PyRulez Feb 21 '15 at 22:42

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.