Timeline for Sheaf cohomology and injective resolutions
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2022 at 17:06 | comment | added | Арсений Кряжев | The last assumption is questionable: math.stackexchange.com/questions/4515688/… | |
| Sep 14, 2011 at 19:14 | history | edited | Anton Geraschenko | CC BY-SA 3.0 |
texified for better readability; added 28 characters in body
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| Jun 9, 2010 at 13:41 | comment | added | Steven Gubkin | This exact development is found in Gunter Harder's book "Lectures on Algebraic Geometry 1". It is also implicit in Hartshorne's treatment but I never knew that "universal delta functors" were as simple as this before reading through Harder's book. I have no idea why this line of thought is not usually presented upfront in presentation of derived functors (Ideally AFTER you have gotten a feeling for some cohomology with your bare hands, such as building $H^1$ from the ground up in group cohomology). Too many people seem content to use the definition without any motivation... | |
| Oct 19, 2009 at 12:53 | comment | added | Tyler Lawson | I'd also like to mention that the reader interested in following this line of thought might read Cartan and Eilenberg's book, which studies homological algebra from pretty basic principles. | |
| Oct 19, 2009 at 9:20 | vote | accept | CommunityBot | ||
| Oct 19, 2009 at 7:02 | comment | added | Greg Stevenson | It is probably worth making explicit that this same argument shows why you can use acyclics for the given functor you are interested in to resolve by and compute derived functors. The splitting property of injectives just ensures that they are suitable for any left exact additive functor. | |
| Oct 19, 2009 at 5:49 | history | answered | Anton Geraschenko | CC BY-SA 2.5 |