14
$\begingroup$

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?

  • 2
    You could look at [the original paper](http://dx.doi.org/10.1090/S0002-9947-1945-0013131-6). There you'll find an extensive discussion and many applications to group theory and topology.2011-11-23
  • 0
    @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.2011-11-23
  • 3
    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](http://www.amazon.com/dp/376437523X)*, here's the table of contents of that chapter: [part 1](http://i.stack.imgur.com/h5cfF.png), [part 2](http://i.stack.imgur.com/itdmt.png) and [here's an extensive review by Corry](http://tau.ac.il/~corry/publications/reviews/pdf/kromer.pdf) of the entire book.2011-11-23
  • 0
    "I didn't invent categories to study functors; I invented them to study natural transformations." - Mac Lane Just some context.2015-02-21

1 Answers 1