Timeline for Models of the Kock-Lawvere axioms
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 11, 2022 at 4:40 | comment | added | მამუკა ჯიბლაძე | Thanks, very interesting. Can one express this in terms of Hilbert schemes of some kind? | |
| Oct 11, 2022 at 1:35 | vote | accept | Alec Rhea | ||
| Oct 10, 2022 at 18:58 | comment | added | user44143 | @მამუკაჯიბლაძე, the ring $R_1$ is richer than it appears, and I think it includes infinitesimals with any of the algebraic properties used in those sources. E.g. $R_1$ contains 4 infinitesimals such that their squares and the product of any 3 are non-zero, even though their cubes are zero and the product of all 4 is zero, such as $w=(t_1+t_2+t_3)(t_4+t_5)$, $x=(t_1+t_2+t_3)(t_6+t_7)$, $y=(t_1+t_2+t_3)(t_8+t_9)$, $z=(t_1+t_2+t_3)(t_{10}+t_{11})$. | |
| Oct 10, 2022 at 15:13 | history | edited | user44143 | CC BY-SA 4.0 |
added link to new question with some evidence of usefulness of this approach
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| Oct 10, 2022 at 12:00 | comment | added | user44143 | @GavinWraith, thanks; I fixed it. | |
| Oct 10, 2022 at 11:58 | history | edited | user44143 | CC BY-SA 4.0 |
fixed typo, paraphrased highlighted sentences, and added to link for counter-classical statement
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| Oct 10, 2022 at 9:58 | comment | added | მამუკა ჯიბლაძე | Seems that there are several inequivalent ways to approach tuples of infinitesimally close points, as witnessed by the work of Breen and Messing in Combinatorial Differential Forms (2001) and Differential Geometry of Gerbes (2005). In particular, infinitesimal neighborhood of the diagonal $X\subset X^n$, infinitesimal cubes, infinitesimal simplices and what they denote by $\Delta^{(n)}$ all seem to be different. | |
| Oct 10, 2022 at 8:36 | comment | added | Gavin Wraith | Isn't there a typo there? Should not "f(d) = cd" be "f(d) = f(0) + cd"? | |
| Oct 9, 2022 at 23:23 | comment | added | Alec Rhea | These are very cool and close to exactly what I was looking for — I’m leaving the question open to see what else crops up, but if it’s still quiet after a few days this is excellent and I’ll accept. Thank you. | |
| Oct 9, 2022 at 22:59 | history | answered | user44143 | CC BY-SA 4.0 |