Timeline for Extending natural transformations of triangulated functors on $D^b(\mathbb P^1)$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 30, 2015 at 11:53 | comment | added | Fernando Muro | That method looks like a pro rather than a con, since the third object is a cone of the first two ones. Can you maybe explain it in your question? | |
| Jan 29, 2015 at 12:50 | comment | added | Francesco Genovese | Actually, "controlling" that is a subtle point. The method I employ to extend the transformation from the two objects $\mathcal O, \mathcal O(1)$ involves dg-enhancements and functorial cones... | |
| Jan 29, 2015 at 10:40 | comment | added | Fernando Muro | But you should have a way of controlling that, right? The third object is not far from the first two ones, and you say you can extend the nat. trans. from those two ones. | |
| Jan 29, 2015 at 10:01 | comment | added | Francesco Genovese | I don't think it should work: I want $\widetilde{\varphi}$ to be equal to $\varphi$ on the specified full subcategory ($\widetilde{\varphi} \circ j = \varphi$). If I restrict $\varphi$ to $\{\mathcal O, \mathcal O(1) \}$ and then extend, I don't know if the obtained extension equals $\varphi$ on $C(x_0)$. | |
| Jan 28, 2015 at 21:08 | comment | added | Fernando Muro | What about restricting and then extending? | |
| Jan 28, 2015 at 17:04 | history | asked | Francesco Genovese | CC BY-SA 3.0 |