Timeline for A conservative, non faithful functor between triangulated categories
Current License: CC BY-SA 3.0
7 events
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| Jun 29, 2015 at 10:15 | comment | added | Mikhail Bondarko | You are always welcome! Sorry for complicated examples; I have just recalled my own experience with these matters. | |
| Jun 28, 2015 at 7:32 | history | edited | Mikhail Bondarko | CC BY-SA 3.0 |
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| Jun 28, 2015 at 7:29 | comment | added | Mikhail Bondarko | Sorry, I was wrong! In my examples all extensions in the heart become trivial; yet the morphisms do not vanish (for simple reasons). I will correct the answer. | |
| Jun 28, 2015 at 6:14 | comment | added | Sasha | I do not know a lot about Hodge modules. But in general, an exact and conservative functor between abelian categories is faithful, I think. For example, in the nLab page "conservative functor", it is said that a functor which is conservative and preserves equalizers, is faithful. | |
| Jun 27, 2015 at 20:16 | history | edited | Mikhail Bondarko | CC BY-SA 3.0 |
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| Jun 27, 2015 at 19:48 | comment | added | Mikhail Bondarko | Certainly, these Hodge examples are far from being "the easiest ones"; one can certainly construct much simpler examples of transversal structures (such that the weight complex functor will not be faithful). I believe that it suffices to consider one of Paranjape's "higher" derived categories of filtered vector spaces here. | |
| Jun 27, 2015 at 19:35 | history | answered | Mikhail Bondarko | CC BY-SA 3.0 |