Timeline for Versions of Choice in categories
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2023 at 18:45 | history | edited | LSpice | CC BY-SA 4.0 |
Unicode; link to paper
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| Jul 2, 2023 at 16:21 | vote | accept | Peter Smith | ||
| Jul 2, 2023 at 5:58 | comment | added | მამუკა ჯიბლაძე | There is also a parametrized version: for any epi $X\to Y$ and any $U$ there is an epi $V\to U$ and a morphism $V\times Y\to X$ with $V\times Y\to X\to Y$ equal to the product projection. | |
| Jul 2, 2023 at 5:18 | answer | added | Mike Shulman | timeline score: 4 | |
| Jun 27, 2023 at 13:28 | comment | added | Peter Smith | OOOPS! Initially I wrote that if a category has Choice-1, it trivially has Choice-2, which was just silly as @Arshak points out, as we only get the trivial implication for the cases where 𝑋≇0! But the remaining case is OK in a topos, say: for then any arrow 0→𝑋 is monic, so an epic 𝑓:0→𝑋 will be iso, since a topos is balanced, and so $f$ will have the required inverse | |
| Jun 27, 2023 at 13:27 | history | edited | Peter Smith | CC BY-SA 4.0 |
deleted 91 characters in body
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| Jun 27, 2023 at 7:47 | history | edited | Peter Smith | CC BY-SA 4.0 |
added 40 characters in body
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| Jun 27, 2023 at 7:33 | comment | added | Arshak Aivazian | I don't think that (1) implies (2) in any category, because for an epimorphism $0 \to Y$ the condition (1) gives no information. So, for example, for the category $\bullet \to \bullet$ condition (1) is trivially satisfied, but (2) is not. | |
| Jun 27, 2023 at 6:11 | history | asked | Peter Smith | CC BY-SA 4.0 |