Timeline for Non-free projective pearls (general and Abelian)
Current License: CC BY-SA 3.0
14 events
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| Mar 27, 2017 at 5:57 | comment | added | Arturo Magidin | @WłodzimierzHolsztyński: I haven't had much time to think about it, beyond noting that none of my examples would work ;-) But you should perhaps add that at the bottom of your original post, rather than hope people will notice it in a comment to an answer. Just note that the addition is made after my answer, so it doesn't appear like I completely missed the point. :-) | |
| Mar 27, 2017 at 4:09 | comment | added | Włodzimierz Holsztyński | Arturo, you (and everybody) is welcome to provide a separate answer (or answers) about the sharp case. | |
| Mar 27, 2017 at 3:18 | comment | added | Włodzimierz Holsztyński | the world is but CHAOS. | |
| Mar 27, 2017 at 2:11 | comment | added | Arturo Magidin | @WłodzimierzHolsztyński: That would certainly get rid of all of my examples, including the proof that an epimorphism must be surjective on the underlying groups (since the maps I construct are not sharp). | |
| Mar 26, 2017 at 8:35 | comment | added | Włodzimierz Holsztyński | I'll call a pearl morphism $\ f: (G\ S)\rightarrow (H\ T)\ $ sharp $\ \Leftarrow:\Rightarrow\ f(S) = T.\ $ Pearls together with sharp pearl morphisms form sharp subcategory of the (full) pearl category. ***** Now, perhaps, the free pearls are projective in the sharp subcategory. (I better finish your answer and check on the sharp subcategory; everybody is welcome to do it and post). | |
| Mar 26, 2017 at 8:20 | comment | added | Włodzimierz Holsztyński | I have read a part of your answer, and I already like it (read upvoted). I need more time to digest all of it. ***** I also somewhat clarified the situation too. I'll present it as a short Answer. | |
| Mar 26, 2017 at 1:50 | history | edited | Arturo Magidin | CC BY-SA 3.0 |
added some comments on what a free object is, and where the proof that free implies projective breaks down.
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| Mar 26, 2017 at 0:34 | history | undeleted | Arturo Magidin | ||
| Mar 26, 2017 at 0:33 | history | edited | Arturo Magidin | CC BY-SA 3.0 |
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| Mar 25, 2017 at 20:00 | history | edited | Arturo Magidin | CC BY-SA 3.0 |
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| Mar 25, 2017 at 7:08 | history | edited | Arturo Magidin | CC BY-SA 3.0 |
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| Mar 25, 2017 at 6:36 | history | edited | Arturo Magidin | CC BY-SA 3.0 |
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| Mar 25, 2017 at 6:30 | history | deleted | Arturo Magidin | via Vote | |
| Mar 25, 2017 at 6:29 | history | answered | Arturo Magidin | CC BY-SA 3.0 |