Timeline for Vopěnka's principle and contravariant full embeddings between module categories
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2021 at 16:09 | vote | accept | Jeremy Rickard | ||
| Jan 19, 2021 at 14:42 | history | edited | Jiří Rosický | CC BY-SA 4.0 |
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| Jan 18, 2021 at 16:30 | comment | added | Jiří Rosický | I have now realized that the same should work for $R$-modules over a commutative ring; see arxiv.org/pdf/1305.3458.pdf. | |
| Jan 18, 2021 at 10:28 | comment | added | Jiří Rosický | Thanks, it is corrected. | |
| Jan 18, 2021 at 10:27 | history | edited | Jiří Rosický | CC BY-SA 4.0 |
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| Jan 18, 2021 at 9:39 | comment | added | Jeremy Rickard | Thanks very much for the details. I think the first sentence of the second paragraph should say "implies WVP is false" rather than "implies WVP"? | |
| Jan 18, 2021 at 9:05 | history | edited | Jiří Rosický | CC BY-SA 4.0 |
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| Jan 18, 2021 at 9:00 | comment | added | Jiří Rosický | No, it works for $\bf{Ab}$ only and uses the result of A. J. Przezdziecki. I will add the argument to my answer. | |
| Jan 17, 2021 at 12:38 | comment | added | Jeremy Rickard | Thanks again. Is it also true that WVP is sufficient to prove that $(\operatorname{Mod}R)^\text{op}$ is not boundable for any ring $R$? | |
| Jan 17, 2021 at 10:02 | comment | added | Jiří Rosický | It seems that it depends on the double dualization on vector spaces. It would be interesting to know what happens for abelian groups. I could show that WVP (weak VP) suffices for $\bf{Ab}$ not being boundable but I do not see that it really depends on set theory. | |
| Jan 17, 2021 at 9:27 | comment | added | Jeremy Rickard | Very interesting, thank you! Does this rely on very special properties of vector spaces, or would you expect a similar statement to be true for arbitrary module categories? | |
| Jan 17, 2021 at 7:09 | history | answered | Jiří Rosický | CC BY-SA 4.0 |