Timeline for Image, kernel, quotient and first isomorphism theorem, in a category of monoid objects
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2014 at 0:48 | comment | added | Dimitri Chikhladze | A first isomorphism theorem for cocommutative Hopf algebras is discussed here projecteuclid.org/euclid.hmj/1206135204 | |
| Nov 3, 2014 at 22:13 | comment | added | Fernando Muro | @SébastienPalcoux well, I don't know, I think I'm influenced by the usual meaning of the work bimodule. | |
| Nov 3, 2014 at 21:10 | vote | accept | Sebastien Palcoux | ||
| Nov 3, 2014 at 10:51 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
addition of the "complety reducible" assumption for the exemple in remark
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| Nov 3, 2014 at 1:57 | comment | added | Sebastien Palcoux | @FernandoMuro: I'm not convinced that for the example of my remark there is no zero object, because (through the subfactors theory), this should be an extension of the category of finite groups: these monoid objects are "group like", not "ring like". | |
| Nov 2, 2014 at 23:34 | comment | added | Fernando Muro | @SébastienPalcoux that of rings, which are monoids in abelian groups. Yours too. | |
| Nov 2, 2014 at 22:54 | comment | added | Sebastien Palcoux | @FernandoMuro: what's the simplest example of category of monoid objects (on a monoidal category) without zero object? | |
| Nov 2, 2014 at 22:48 | comment | added | Sebastien Palcoux | @ZhenLin: the unit object $\mathbb{Z}$ of Ab is not a zero object, but Ab has the zero object $\{ e \}$. | |
| Nov 2, 2014 at 22:19 | comment | added | Fernando Muro | @QiaochuYuan neither Sébastien nor I. | |
| Nov 2, 2014 at 22:18 | comment | added | Qiaochu Yuan | Oh, I assumed that Fernando meant monoids in $\text{Set}$. | |
| Nov 2, 2014 at 22:18 | comment | added | Zhen Lin | @QiaochuYuan The trivial monoid with respect to a cartesian monoidal structure is a zero object, yes. But consider for instance $\mathbb{Z}$ as a monoid in $\mathbf{Ab}$... | |
| Nov 2, 2014 at 22:18 | answer | added | Qiaochu Yuan | timeline score: 17 | |
| Nov 2, 2014 at 22:17 | comment | added | Fernando Muro | @QiaochuYuan try to check that it's initial. | |
| Nov 2, 2014 at 22:16 | comment | added | Qiaochu Yuan | @Fernando: hmm? The trivial monoid is surely the zero object. | |
| Nov 2, 2014 at 22:15 | comment | added | Fernando Muro | There's no zero object in the category of monoids. | |
| Nov 2, 2014 at 22:12 | comment | added | Sebastien Palcoux | @FernandoMuro: Nice! And what about the first isomorphism theorem? | |
| Nov 2, 2014 at 22:11 | comment | added | Fernando Muro | Well, you're asking about notions which make sense (although they may not exist) in arbitrary categories with zero object. | |
| Nov 2, 2014 at 21:49 | history | asked | Sebastien Palcoux | CC BY-SA 3.0 |