Timeline for Exactness of pure functors
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 26, 2015 at 11:11 | comment | added | Mikhail Bondarko | Possibly, you can benefit from Appendix D in users.unimi.it/~barbieri/der1mot.pdf | |
| Jan 25, 2015 at 21:15 | comment | added | Mostafa - Free Palestine | @DanPetersen The graded quotient functors are exact by the definition of mixed categories ( morphisms are strict) | |
| Jan 25, 2015 at 20:55 | comment | added | Dan Petersen | To be explicit, a functor which is the identity on pure objects but is not exact is given by mapping $V \stackrel f \to W$ to $\ker(f) \stackrel 0 \to \mathrm{coker}(f)$. Another possible fix than Jeremy Rickard's suggestion might be to impose the condition that the functors $\mathrm{gr}^W_i$ are exact. (This is just a suggestion, I don't know if the lemma holds under either added hypothesis.) | |
| Jan 25, 2015 at 20:26 | comment | added | Mostafa - Free Palestine | @JeremyRickard Yes, this is a reasonable condition and works. I was not confident on my example and so presented it here as a question. | |
| Jan 25, 2015 at 20:12 | history | edited | Jeremy Rickard | CC BY-SA 3.0 |
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| Jan 25, 2015 at 20:04 | comment | added | Jeremy Rickard | I agree that, with the definitions as stated in the paper, your example works. Maybe the definition of a pure functor is meant to include the condition that it commutes with the functors $M\mapsto W_iM$ and $M\mapsto M/W_iM$ (which is not the case in your example). Would that make sense? | |
| Jan 25, 2015 at 19:11 | history | edited | Mostafa - Free Palestine | CC BY-SA 3.0 |
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| Jan 25, 2015 at 13:11 | history | edited | Mostafa - Free Palestine | CC BY-SA 3.0 |
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| Jan 25, 2015 at 12:13 | history | asked | Mostafa - Free Palestine | CC BY-SA 3.0 |