Timeline for When forgetting structure doesn't matter
Current License: CC BY-SA 4.0
29 events
| when toggle format | what | by | license | comment | |
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| Jan 5, 2023 at 0:20 | answer | added | Martin Brandenburg | timeline score: 2 | |
| May 4, 2022 at 0:34 | answer | added | Anton Izosimov | timeline score: 0 | |
| May 1, 2022 at 20:36 | answer | added | Peter LeFanu Lumsdaine | timeline score: 5 | |
| May 1, 2022 at 6:59 | answer | added | Kevin Carlson | timeline score: 9 | |
| Apr 30, 2022 at 21:47 | answer | added | Andrea Marino | timeline score: 2 | |
| Apr 30, 2022 at 20:58 | answer | added | André Henriques | timeline score: 5 | |
| Apr 30, 2022 at 20:47 | answer | added | Joseph Van Name | timeline score: 2 | |
| Apr 30, 2022 at 18:41 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Apr 30, 2022 at 16:46 | answer | added | Terry Tao | timeline score: 23 | |
| Apr 30, 2022 at 16:10 | answer | added | Tim Campion | timeline score: 12 | |
| Apr 30, 2022 at 14:33 | answer | added | Rodrigo Freire | timeline score: 4 | |
| Apr 30, 2022 at 13:13 | answer | added | Qfwfq | timeline score: 1 | |
| Apr 30, 2022 at 11:08 | answer | added | Maxime Ramzi | timeline score: 18 | |
| Apr 30, 2022 at 9:44 | answer | added | R. van Dobben de Bruyn | timeline score: 8 | |
| Apr 30, 2022 at 8:44 | answer | added | Dmitry Vaintrob | timeline score: 12 | |
| Apr 30, 2022 at 8:21 | history | became hot network question | |||
| Apr 30, 2022 at 6:17 | answer | added | Gregory Arone | timeline score: 32 | |
| Apr 30, 2022 at 1:47 | comment | added | Alec Rhea | @A.S. That sounds promising, nice idea. | |
| Apr 30, 2022 at 1:33 | comment | added | Sam Hopkins | @A.S.: So maybe we get an example from $C^1$ manifolds vs. $C^\infty$ or even $C^{\omega}$ manifolds? | |
| Apr 30, 2022 at 1:31 | comment | added | user164898 | I suppose one type of example comes about whenever an object specified by a wishlist of nice properties turns out to be uniquely determined by those properties. For example you could consider the category of Riemannian manifolds equipped with a torsion-free connection compatible with the metric. Then the forgetful functor to Riemannian manifolds is an isomorphism of categories, since the Levi-Civita connection is the only such connection (but of course this fact is nontrivial). Probably more interesting examples would be those that given an equivalence of categories rather than an isomorphism. | |
| Apr 30, 2022 at 1:28 | comment | added | Alec Rhea | @paulgarrett Yes, that would be another way to view it. | |
| Apr 30, 2022 at 0:54 | comment | added | paul garrett | @AlecRhea, so you're meaning to ask about something like "redundant structure"? :) | |
| Apr 30, 2022 at 0:49 | history | edited | Alec Rhea |
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| Apr 30, 2022 at 0:44 | comment | added | Alec Rhea | @SamHopkins That is interesting, but Noah is correct that I would also like essential surjectivity to hold so that every object in the target category of the forgetful functor 'looks like' something we forgot the structure of in its domain. | |
| Apr 30, 2022 at 0:26 | comment | added | Noah Schweber | @SamHopkins I don't think it does constitute an example of not forgetting anything in the sense that the OP's asking about: while in a sense it doesn't forget anything about individual objects (being fully faithful), it forgets a lot about the global nature of the source category. | |
| Apr 30, 2022 at 0:25 | comment | added | Sam Hopkins | Right, of course. But it is an example of a forgetful functor that "doesn't forget anything." | |
| Apr 30, 2022 at 0:24 | comment | added | Noah Schweber | @SamHopkins That functor is fully faithful, but it's not an equivalence. | |
| Apr 30, 2022 at 0:20 | comment | added | Sam Hopkins | Howabout something like the forgetful functor from abelian groups to groups? | |
| Apr 30, 2022 at 0:17 | history | asked | Alec Rhea | CC BY-SA 4.0 |