Timeline for A similar construction to Ext, can we describe it better and does it have any use?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 12, 2021 at 12:27 | vote | accept | kevkev1695 | ||
| Apr 12, 2021 at 5:24 | comment | added | Jochen Wengenroth | Similar question (without answer): mathoverflow.net/questions/387352/… | |
| Apr 11, 2021 at 21:32 | history | became hot network question | |||
| Apr 11, 2021 at 16:42 | answer | added | Bertram Arnold | timeline score: 8 | |
| Apr 11, 2021 at 15:50 | history | edited | kevkev1695 | CC BY-SA 4.0 |
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| Apr 11, 2021 at 15:41 | comment | added | kevkev1695 | Yes, in this case $F^0 $ equals the tensor product again, because it is right-exact. | |
| Apr 11, 2021 at 15:40 | comment | added | Zerox | The widely used dual functor of $\text{Ext}$ is $\text{Tor}$, which differs from your definition by changing $\text{Hom}_R(X,-)$ into $-\otimes_{R}X$ and swaps $X$ and $Y$. | |
| Apr 11, 2021 at 15:28 | history | edited | kevkev1695 | CC BY-SA 4.0 |
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| Apr 11, 2021 at 15:21 | comment | added | kevkev1695 | It should be well-defined, because two different projective resolutions are homotopy equivalent, so applying $\text{Hom}(X,-)$ should yield again two homotopy equivalent chain complexes since the functor is additive. | |
| Apr 11, 2021 at 15:13 | comment | added | John Palmieri | Why is this well-defined? | |
| Apr 11, 2021 at 13:31 | history | asked | kevkev1695 | CC BY-SA 4.0 |