Timeline for How to formally split monomorphisms nicely?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 22, 2017 at 9:51 | vote | accept | Chris Heunen | ||
| Sep 20, 2017 at 18:58 | comment | added | Qiaochu Yuan | An important difference between splitting monomorphisms and splitting idempotents is that splittings of idempotents, when they exist, have a universal property, and hence are unique up to unique isomorphism. Even more, their universal property uniquely determines both morphisms into and out of them. But splittings of monomorphisms are far from unique and there's no universal property in sight. | |
| Sep 20, 2017 at 17:30 | comment | added | Gejza Jenča | If $\mathcal C$ is a category with coproducts, then there is a monad on the arrow category $\mathcal C^{\rightarrow}$ such that the category of algebras for that monad is exactly the category of split monomorphisms equipped with a chosen retraction. | |
| Sep 20, 2017 at 16:01 | answer | added | Simon Henry | timeline score: 8 | |
| Sep 20, 2017 at 15:31 | comment | added | Simon Henry | I assume that just freely adding retraction wouldn't qualify as elegant ? | |
| Sep 20, 2017 at 15:25 | history | asked | Chris Heunen | CC BY-SA 3.0 |