Timeline for History of "natural transformations"
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Dec 21, 2017 at 20:53 | answer | added | Vladimir Dotsenko | timeline score: 2 | |
| Dec 21, 2017 at 20:33 | vote | accept | Mahdi Majidi-Zolbanin | ||
| Dec 21, 2017 at 19:43 | comment | added | KConrad | Okay, I have done that now. | |
| Dec 21, 2017 at 19:43 | answer | added | KConrad | timeline score: 14 | |
| Dec 21, 2017 at 17:36 | comment | added | Mahdi Majidi-Zolbanin | @KConrad Interestingly, he also speaks of natural topology and natural neighborhoods, which I don't think fit in the context of natural transformation of functors. In any case, if you post your comment as an answer, I will accept it, so that this question doesn't seem like unanswered. | |
| Dec 21, 2017 at 17:32 | comment | added | Mahdi Majidi-Zolbanin | @KConrad I received Whitney's paper and finally got a chance to take a look. Indeed he uses the term natural isomorphism several times. For example, after he defines tensor product of abelian groups, he states that if $A$ and $B$ are abelian groups, then there is a natural isomorphism $A\otimes B\stackrel{\sim}{\rightarrow}B\otimes A$ (in his notation he uses $\circ$ instead of $\otimes$). This is indeed consistent with the notion of natural isomorphism of functors, as one can consider it an isomorphism of functors $\cdot\otimes B$ and $B\otimes\cdot$, for any fixed abelian group $B$. | |
| Dec 8, 2017 at 1:42 | comment | added | Mahdi Majidi-Zolbanin | @KConrad: Thank you! I didn't have immediate access to that article. I requested it. I will probably receive it in a few days and can respond. | |
| Dec 7, 2017 at 1:28 | comment | added | KConrad | See Whitney's paper from 1935 where he defined tensor products of abelian groups (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. | |
| Dec 7, 2017 at 1:13 | comment | added | Mahdi Majidi-Zolbanin | @KConrad I do not object! If you can provide an instance in algebra prior to the work of Eilenberg and Mac Lane, where a homomorphism is referred to as being "natural" and really means natural, I will take it! | |
| Dec 7, 2017 at 1:04 | comment | added | KConrad | Why do you object to the use of "natural homomorphism" as what Kromer had in mind? The notion of naturality was use earlier in algebra before any work of Eilenberg and Mac Lane, not the specific term "natural transformation". You are reading too much into things. | |
| Dec 7, 2017 at 0:56 | history | edited | Mahdi Majidi-Zolbanin | CC BY-SA 3.0 |
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| Dec 7, 2017 at 0:46 | comment | added | Mahdi Majidi-Zolbanin | @Eric I am asking about the use of the phrase "natural transformation", not things that could now be called natural transformations. I will edit to make it clear. | |
| Dec 7, 2017 at 0:33 | comment | added | Eric Towers | Are you asking about use of the phrase "natural transformation" and its syntactic variants, or are you asking about instances of things which could now be called natural transformations? When you say "use of the notion", you seem to be asking for the latter, but your comments to the current answer suggest that you are pursuing the former. | |
| Dec 6, 2017 at 21:38 | comment | added | Mahdi Majidi-Zolbanin | Did anyone refer to determinant as a natural transformation before 1942? | |
| Dec 6, 2017 at 21:29 | comment | added | Carlo Beenakker | it can be argued that the determinant is a natural transformation; does that count? (natural transformation in the sense of "not depending on choice of basis" obviously goes back way before 1940...) | |
| Dec 6, 2017 at 20:59 | history | edited | Mahdi Majidi-Zolbanin | CC BY-SA 3.0 |
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| Dec 6, 2017 at 20:41 | history | edited | Mahdi Majidi-Zolbanin | CC BY-SA 3.0 |
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| Dec 6, 2017 at 18:07 | answer | added | Carlo Beenakker | timeline score: 12 | |
| Dec 6, 2017 at 16:48 | history | asked | Mahdi Majidi-Zolbanin | CC BY-SA 3.0 |