Timeline for Is the composite of absolute derived functors a derived functor?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 26, 2023 at 18:44 | comment | added | D.-C. Cisinski | I never claim anything like (a) in my book. However, I revisit all this kind of things later in the book; there is formula (7.5.25.3) on 382 page that is a correct replacement of (a). This is at the heart of Maltiniotis' proof of derived adjunctions. | |
| Jul 17, 2022 at 10:49 | vote | accept | carciofo21 | ||
| Jul 17, 2022 at 8:14 | answer | added | Zhen Lin | timeline score: 6 | |
| Jul 16, 2022 at 18:26 | comment | added | carciofo21 | @ZhenLin I see. Are the counterexamples supposed to be obvious? | |
| Jul 16, 2022 at 12:09 | comment | added | Zhen Lin | That's a different definition of deformable functor. The original DHKS definition does not require that the image of an object in the "deformation retract" of the domain category to be an object in the "deformation retract" of the codomain category. (This is the compatibility condition I was alluding to.) | |
| Jul 16, 2022 at 11:32 | comment | added | carciofo21 | See, for instance, Thm 2.2.9 in Categorical homotopy theory by Riehl | |
| Jul 16, 2022 at 11:27 | comment | added | carciofo21 | @ZhenLin is that beacuse such a composite is not an absolute derived functor or does it fail to be also a plain one? I thought this was true for derived functors built with deformations, though. | |
| Jul 16, 2022 at 10:31 | comment | added | Zhen Lin | It is not true that composing absolute derived functors results in an absolute derived functor, not even if you construct them using deformations. There is a compatibility condition that is automatically satisfied when you have Quillen functors and use (co)fibrant replacements, though. | |
| Jul 15, 2022 at 18:25 | history | edited | carciofo21 | CC BY-SA 4.0 |
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| Jul 15, 2022 at 17:48 | history | edited | carciofo21 | CC BY-SA 4.0 |
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| S Jul 15, 2022 at 17:43 | review | First questions | |||
| Jul 15, 2022 at 20:34 | |||||
| S Jul 15, 2022 at 17:43 | history | asked | carciofo21 | CC BY-SA 4.0 |