Timeline for injectivity of pushout?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 10, 2020 at 13:02 | answer | added | Robbie Lyman | timeline score: 2 | |
| May 6, 2020 at 21:29 | comment | added | Philippe Gaucher | @qkqh I've learnt something today, I could not imagine that there would be a counterexample. In my mind, a group is a one-object category, and the pushout must contain all possible compositions. | |
| May 6, 2020 at 20:34 | history | edited | David Roberts♦ |
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| May 6, 2020 at 17:32 | history | edited | qkqh | CC BY-SA 4.0 |
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| May 6, 2020 at 17:23 | history | edited | qkqh | CC BY-SA 4.0 |
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| May 6, 2020 at 16:52 | comment | added | qkqh | @PhilippeGaucher What does it mean to add the free compositions in the category of groups? Could you explain it in detail? | |
| May 6, 2020 at 16:44 | comment | added | qkqh | @MaximeRamzi I found that the above injectivity holds in any topos (toposes are adhesive). I cannot understand what topos is, but I think it may provide some answer. If topos theory has nothing to do with my question, sorry. Then, tell me. I will subtract it. | |
| May 6, 2020 at 11:55 | comment | added | Maxime Ramzi | What has this got to do with topos theory ? | |
| May 6, 2020 at 9:54 | comment | added | Philippe Gaucher | The pushout of a one-to-one map in the category of sets is one-to-one. In the category of groups, my guess is that you have to add the free compositions. So I would be surprised that $f$ is not one-to-one. | |
| May 6, 2020 at 9:47 | history | asked | qkqh | CC BY-SA 4.0 |