I am looking for the source (and original version) of the above oft-repeated quotation. Mac Lane mentions it in Categories for the Working Mathematician, attributing it to Eilenberg-Mac Lane; however, I didn't see it while briefly skimming their paper General Theory of Natural Equivalences.


1 Answer 1


CW since some of the recent posts on MO have required little more than googling.

Prior to the book you mentioned, MacLane attributed this saying to Peter Freyd in:

MacLane, S. (1965). Categorical algebra. Bulletin of the American Mathematical Society, 71(1), 40-106.

Relevant excerpt: (p. 48)

enter image description here

With regard to the original language, Eric Wofsey points out that Freyd's Abelian Categories (1964) begins with this description:

enter image description here

  • 3
    $\begingroup$ Freyd makes this statement on this first page of his book Abelian categories: "It is not too misleading, at least historically, to say that categories are what one must define in order to define functors, and that functors are what one must define in order to define natural transformations." $\endgroup$ Oct 2, 2013 at 4:47
  • $\begingroup$ Great; I've added in an image from page 1 of Freyd's book. $\endgroup$ Oct 2, 2013 at 4:56
  • 4
    $\begingroup$ Is it no true that the "serious disservice" to which Peter Freyd refers is committed in a number of text books? $\endgroup$ Oct 2, 2013 at 14:45

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