Timeline for Pullback and pseudoelements
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2022 at 14:56 | comment | added | Ricky | The formalization of the counterexample is here. | |
| Apr 11, 2022 at 21:12 | comment | added | Ricky | I just want to add that I've formally verified your answer, and it's correct. | |
| Apr 9, 2022 at 12:47 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 4.0 |
Removed hedging from headline; and tightened up proof of key claim
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| Apr 9, 2022 at 9:27 | vote | accept | Ricky | ||
| Apr 8, 2022 at 17:38 | comment | added | Peter LeFanu Lumsdaine | @Ricky: Since the answer is so disputed, I’ll wait till we’ve both slept on this, and if we still both stand by this answer in the morning, I’ll post it on the math.stackexchange question as well. | |
| Apr 8, 2022 at 17:28 | comment | added | Ricky | I will accept your answer tomorrow after a good sleep (just to be 100% sure, but I don't see any possible problem in it). You can post an answer also to the stackechange question if you want. | |
| Apr 8, 2022 at 17:24 | comment | added | Peter LeFanu Lumsdaine | @Ricky: thanks for pointing out that error! Have fixed it there — tersely in text since as you note it’s not needed, but in full here: Given pseudo-elements $x_i \colon X_i \to X$ with the same image, take the cover of the image by the free module on the underlying sets $X_1 \amalg X_2$. Then this cover factors through each $x_i$. | |
| Apr 8, 2022 at 17:20 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 4.0 |
fixed error pointed out in comments
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| Apr 8, 2022 at 17:18 | comment | added | Ricky | It's possible that Borceux had something else in mind, indeed at the end of 1.9 he says "equivalence classes of pseudo-elements", but pseudoelements are already equivalences classes, so there is maybe another relation to take into account. In any case I agree that the claim that the two pseudoelements are equal is false. | |
| Apr 8, 2022 at 17:15 | comment | added | Ricky | A minor point: in you explanation it's not clear why the morphisms from the projective cover of the image to the two objecs are epi, but it's not important (even if we can made them epi without troubles), it's the other implication that is needed here. | |
| Apr 8, 2022 at 17:14 | comment | added | Ricky | OMG, thank you!! Lesson learnt: don't waste hours trying to prove a theorem without looking for a counterexample. | |
| Apr 8, 2022 at 17:07 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 4.0 |
explicitly rephrased counterexample in terms of pseudo-elements
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| Apr 8, 2022 at 17:01 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 4.0 |
bolded key observation
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| Apr 8, 2022 at 16:52 | history | answered | Peter LeFanu Lumsdaine | CC BY-SA 4.0 |