(Edit #1 after Carlo's response)


It is often claimed that *the notion of natural transformations existed in mathematical vocabulary long before it had a definition*. In fact, I quoted the statement in *italic* from [1, p. 2]. As another example, in [2, p. 70] Ralf Kromer says: *The claim is that there was, at the time when [3] was written, a current informal parlance consisting in calling certain transformations natural and that Mac Lane and Eilenberg tried (and succeeded) to grasp this informal parlance mathematically*. 


Three years after [3], Eilenberg and Maclane discovered the fact that this notion could be mathematically defined in [4]. 


However, Ralf Kromer casts doubt on the above mentioned claim, due to lack of evidence (see: [2, p. 70]).


(Edit #2 after Eric's comment) My question is, can you supply an evidence of use of the phrase "natural transformations" or its variants in mathematical literature prior to [3]? I must add that in [2] Kromer gives a number of examples of use of phrases such as "natural homomorphism" or "natural projection" in the literature prior to or around the same time as [3], but in each case they turn out to have different meanings. So I am asking for example(s) of use of the phrase "natural transformations", which are really natural transformations.


**References:**


1. Peter Freyd: **Abelian Categories** (1964).
2. Ralf Kromer: **Tool and Object: a history and philosophy of category theory** (2007).
3. Samuel Eilenberg and Saunders Maclane: *Group extensions and homology*, Annals Math. (2) **43**, p.p. 757–831 (1942).
4. Samuel Eilenberg and Saunders Maclane: *General theory of natural transformations*, Trans. AMS, **58**, p.p.: 231-294 (1945).



History of "natural transformations"
See Whitney's [paper from 1935 where he defined tensor products of abelian groups](http://projecteuclid.org/download/pdf_1/euclid.dmj/1077490789). There you will find the terms natural homomorphism and (especially) natural isomorphism. Whitney makes no attempt to give absolutely rigorous definitions of those concepts, as the motivation to do so was lacking, but his sense of "naturality" is what Eilenberg and Mac Lane were making precise in their introduction of natural transformations. 


