Timeline for Who introduced nerves in category theory?
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20 events
| when toggle format | what | by | license | comment | |
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| Dec 6, 2021 at 5:12 | vote | accept | user234212323 | ||
| Dec 6, 2021 at 2:38 | comment | added | user470562 | I'd remark that we have a highly related (though not exactly the same) question on the nerve construction's use in algebraic topology here in case it's of interest: mathoverflow.net/questions/98824/origins-of-the-nerve-theorem. | |
| Dec 6, 2021 at 1:25 | comment | added | David Roberts♦ | DOI link for Alexandroff's article: doi.org/10.1007/BF01451612, (and free pdf link: maths.ed.ac.uk/~v1ranick/papers/alexdim.pdf). I wonder if he talked with Noether about this stuff... | |
| Dec 6, 2021 at 1:23 | history | became hot network question | |||
| Dec 5, 2021 at 21:28 | comment | added | D.-C. Cisinski | @DmitriPavlov Thanks! | |
| Dec 5, 2021 at 20:24 | comment | added | Dmitri Pavlov | @D.-C.Cisinski: Nerves of covers were introduced by Paul Alexandroff in his 1928 paper Über den allgemeinen Dimensionsbegriff und seine Beziehungen zur elementaren geometrischen Anschauung. | |
| Dec 5, 2021 at 16:49 | answer | added | Thomas Holder | timeline score: 11 | |
| Dec 5, 2021 at 16:20 | comment | added | Benjamin Steinberg | @D.-C.Cisinski Segal doesn't claim originality. I don't know the history well enough. Gabriel and Zisman is a similar time period I have no idea which was drafted first or what Gothendieck explicitly did. But many papers do claim Segal's paper as an original reference | |
| Dec 5, 2021 at 15:43 | comment | added | D.-C. Cisinski | I do not know which paper introduced nerves first, but I think the first textbook is Gabriel and Zisman's Calculus of Fractions and Homotopy Theory, Springer, 1967 (they discuss nerves in full generality for sure). | |
| Dec 5, 2021 at 15:35 | comment | added | D.-C. Cisinski | @BenjaminSteinberg My comment on Segal and Grothendieck stands: they did not introduce nerves. | |
| Dec 5, 2021 at 15:24 | comment | added | Benjamin Steinberg | @D.-C.Cisinski the question is asking who introduced nerves of categories not nerves of coverings which undoubtedly goes back to cech. | |
| Dec 5, 2021 at 15:22 | comment | added | D.-C. Cisinski | @BenjaminSteinberg Segal and Grothendieck did not introduce nerves: they introduced the idea of characterizing which simplicial sets are isomorphic to nerves. It is definitely Čech who introduced nerves of coverings. | |
| Dec 5, 2021 at 15:21 | comment | added | Benjamin Steinberg | I think this paper is usually cited numdam.org/article/PMIHES_1968__34__105_0.pdf | |
| Dec 5, 2021 at 13:37 | comment | added | HJRW | In the context of algebraic topology, nerves play a fundamental role in the definition of Čech cohomology. The nLab asserts (ncatlab.org/nlab/show/%C4%8Cech+nerve) that this is how Čech gave his definition, presumably in the 1930s. | |
| Dec 5, 2021 at 12:11 | comment | added | Benjamin Steinberg | Maybe G. Segal did but attributes it too Grothendieck | |
| Dec 5, 2021 at 5:15 | comment | added | Wlod AA | Eilenberg-Zilber? | |
| Dec 5, 2021 at 3:19 | review | Close votes | |||
| Dec 12, 2021 at 3:11 | |||||
| Dec 5, 2021 at 2:58 | comment | added | LSpice | This would be better on hsm.stackexchange.com. | |
| Dec 5, 2021 at 2:58 | history | edited | LSpice | CC BY-SA 4.0 |
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| Dec 5, 2021 at 2:23 | history | asked | user234212323 | CC BY-SA 4.0 |