Timeline for Fourier--Mukai transforms and adjunction
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 23, 2014 at 5:43 | vote | accept | Nathaniel Bottman | ||
| Nov 28, 2013 at 3:22 | answer | added | Sasha | timeline score: 5 | |
| Nov 27, 2013 at 22:18 | answer | added | Dan Petersen | timeline score: 5 | |
| Nov 27, 2013 at 22:17 | history | edited | Nathaniel Bottman | CC BY-SA 3.0 |
added 85 characters in body
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| Nov 27, 2013 at 22:16 | comment | added | Nathaniel Bottman | @QiaochuYuan thanks! If preservation of limits and colimits is an important consequence, then I will try and think about what that means for the derived category of coherent sheaves. I guess I failed to mention in my question that what I'm really interested in is geometric consequences for $D^b$, not "abstract nonsense consequences" that always happen when both $(F,G)$ and $(G,F)$ are adjoint pairs. | |
| Nov 27, 2013 at 22:02 | comment | added | Qiaochu Yuan | Consider also the example of the diagonal functor $C \to C^2$. The left adjoint of the diagonal, if it exists, is the coproduct. The right adjoint, if it exists, is the product. They agree iff $C$ has biproducts, which is a very special property and in particular implies that $C$ is canonically enriched over commutative monoids. | |
| Nov 27, 2013 at 21:59 | comment | added | Qiaochu Yuan | It tells you that $F$ and $G$ both preserve both colimits and limits! | |
| Nov 27, 2013 at 21:57 | history | asked | Nathaniel Bottman | CC BY-SA 3.0 |