Timeline for Compact object and compact generator in a category
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 25, 2020 at 6:56 | answer | added | Qiaochu Yuan | timeline score: 15 | |
| Nov 24, 2020 at 22:29 | history | became hot network question | |||
| Nov 24, 2020 at 17:11 | comment | added | Ryze | @ToddTrimble thank you! | |
| Nov 24, 2020 at 17:07 | history | edited | Ryze | CC BY-SA 4.0 |
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| Nov 24, 2020 at 17:03 | comment | added | Todd Trimble | Oh, I see your difficulty. You should just use Paquette's definition and add the Murfet-compactness condition to it (or the Lurie-compactness condition, depending on what you are trying to do). I think a more conceptual way of defining Murfet-compactness is that an object $M$ is compact if $\hom(M, -): C \to Ab$ preserves coproducts (we're assuming here, as I think Murfet intends, that our categories here are $Ab$-enriched). | |
| Nov 24, 2020 at 16:27 | comment | added | Ryze | @ToddTrimble I am looking for a general definition of compact generator. A compact generator is a compact object, but the definition of compact generator I gave does not seem to fit the definition of compact object. | |
| Nov 24, 2020 at 16:10 | comment | added | Todd Trimble | I'm not sure what your second question is trying to ask. In $R$-Mod, $R$ is a compact generator since every $R$-module is a quotient of a free $R$-module (a coproduct of copies of $R$). What else are you looking for? | |
| Nov 24, 2020 at 15:17 | history | edited | Ryze | CC BY-SA 4.0 |
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| Nov 24, 2020 at 15:10 | answer | added | Mike Shulman | timeline score: 9 | |
| Nov 24, 2020 at 14:43 | answer | added | Todd Trimble | timeline score: 12 | |
| Nov 24, 2020 at 14:25 | history | asked | Ryze | CC BY-SA 4.0 |