Timeline for Examples of five-adjoint systems
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 16, 2022 at 8:10 | comment | added | Maxime Ramzi | A reference for which part exactly ? for the general statement about $B/A$ I'm not sure, but for co/induction, any introductory document to representation theory should introduce these :) | |
| May 16, 2022 at 1:35 | history | edited | Simon Henry | CC BY-SA 4.0 |
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| May 15, 2022 at 18:11 | comment | added | Alexander Praehauser | @MaximeRamzi Thanks! Could you give me a reference? | |
| May 15, 2022 at 17:40 | history | edited | LSpice | CC BY-SA 4.0 |
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| May 15, 2022 at 16:58 | comment | added | Maxime Ramzi | But also, for induction/co-induction, there is no need for them to be isomorphic : if $B$ is an $A$-algebra which is f.g. projective as an $A$-module, then the the left and right adjoint to the forgetful functor $Mod_B\to Mod_A$ always have adjoints themselves | |
| May 15, 2022 at 16:55 | comment | added | Maxime Ramzi | Just for clarification : e right/left adjoint to the forgetful are not fixed point and co-fixed point, but induction and co-induction, and they are isomorphic as soon as $G$ is finite (fixed points and orbits are right/left adjoint to the "trivial representation" functor, and these are indeed only isomorphic if $|G|\in k^\times$) | |
| May 15, 2022 at 16:36 | history | edited | Simon Henry | CC BY-SA 4.0 |
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| May 15, 2022 at 16:14 | history | answered | Simon Henry | CC BY-SA 4.0 |