Timeline for localizing subcategories of a nice triangulated category
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Mar 7, 2021 at 16:02 | vote | accept | lab | ||
| Mar 7, 2021 at 14:54 | answer | added | Drew Heard | timeline score: 4 | |
| Mar 7, 2021 at 14:52 | comment | added | Fernando Muro | @DrewHeard you're right, so it's just that $i$ doesn't preserve products. | |
| Mar 7, 2021 at 14:30 | comment | added | Drew Heard | @FernandoMuro For $Y,\{X_i\} \in \text{Loc}(b)$ we have $[Y,W \prod_i {X_i}] = [i(Y),\prod {X_i}] = \prod_i [i(Y),X_i] = \prod_i [Y,W(X_i)]$. So I think the product is just the product in $D(A)$ followed by $W$. | |
| Mar 6, 2021 at 23:26 | comment | added | Fernando Muro | @DrewHeard does that localizing subcategory even have products? | |
| Mar 6, 2021 at 17:14 | history | edited | lab | CC BY-SA 4.0 |
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| Mar 6, 2021 at 10:18 | history | undeleted | lab | ||
| Mar 5, 2021 at 20:31 | history | deleted | lab | via Vote | |
| Mar 5, 2021 at 18:45 | comment | added | Drew Heard | Is there any reason to suspect this is true? Take $A = D(R)$ for, say, a Noetherian regular local ring $(R,\mathfrak{m},k)$, and take $b = k$. The localizing subcategory generated by $k$ is then the derived category $\mathfrak{m}$-torsion $R$-modules. The inclusion will not, in general, preserve limits. | |
| Mar 5, 2021 at 18:44 | history | edited | lab | CC BY-SA 4.0 |
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| Mar 5, 2021 at 18:35 | history | edited | lab | CC BY-SA 4.0 |
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| Mar 5, 2021 at 18:27 | history | asked | lab | CC BY-SA 4.0 |