Timeline for Categorical setting for cancellation in direct sums
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| May 2, 2021 at 11:57 | comment | added | Filippo Alberto Edoardo | @LSpice Thanks! | |
| May 1, 2021 at 18:54 | comment | added | user127776 | You might need to look at Krull-Schmidt categories, they satisfy this property. | |
| May 1, 2021 at 18:51 | comment | added | Tim Campion | I'm more familiar with formal non-cancellation arguments like the Eilenberg swindle. Even when everything is "suitably finite", non-cancellation shows up when talking about stably-free modules and bundles, for example. OTOH I suppose if everything is free and finitely-generated, then one is talking about Invariant Basis Number rings, among which are all commutative rings. I think cancellation may also hold in an Artinian abelian category? | |
| May 1, 2021 at 18:51 | comment | added | LSpice | I edited in a link to the Swan paper. Do you have a reference for the theorem of Cohn and Walker? | |
| May 1, 2021 at 18:51 | history | edited | LSpice | CC BY-SA 4.0 |
Link to Swan's paper
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| May 1, 2021 at 18:49 | comment | added | Filippo Alberto Edoardo | @TimCampion Thanks, you are right! I have modified and corrected the statement. | |
| May 1, 2021 at 18:48 | history | edited | Filippo Alberto Edoardo | CC BY-SA 4.0 |
Corrected following a comment by Tim Cambion
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| Apr 30, 2021 at 22:28 | comment | added | Tim Campion | For finitely-generated abelian groups, or finitely-generated modules over a PID, doesn't this follow directly from the classification thereof? Perhaps the theorem of Cohn and Walker is meant to refer to something else? | |
| Apr 30, 2021 at 11:56 | history | asked | Filippo Alberto Edoardo | CC BY-SA 4.0 |