Timeline for How to compute cup product of derived limits / presheaf cohomology
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2021 at 15:19 | comment | added | Dmitri Pavlov | @Mr.Palomar: A more explicit description of the source resolution can only be given for a more explicit description of the category C. | |
| Jan 12, 2021 at 14:49 | comment | added | Dmitri Pavlov | @Mr.Palomar: The Yoneda pairing is not the cup product, the link was giving an example how to resolve the source instead of the target. An explicit description of the cofibrant replacement functor is given in the last sentence: it is the bar construction applied to the free-forgetful adjunction between Ob(C)-indexed chain complexes over k and presheaves of chain complex over k on C. | |
| Jan 12, 2021 at 14:46 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
added 31 characters in body
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| Jan 12, 2021 at 14:21 | comment | added | Mr. Palomar | Perhaps I should add that the sheaves I'm interested in take values not merely in rings but in $k$-algebras, for $k$ a field, which means that the underlying $j$-th graded pieces produce vector spaces. This gives it a more 'combinatorial' flavour, and for this reason I'm hoping that something like GAP or Sage has the capacity to take over the work of finding the resolutions. | |
| Jan 12, 2021 at 14:10 | comment | added | Mr. Palomar | Is the link really talking about the same thing? There is always a Yoneda pairing $\operatorname{Ext}^p(\mathcal{F},\mathcal{G}) \otimes \operatorname{Ext}^q(\mathcal{G},\mathcal{H}) \to \operatorname{Ext}^{p+q}(\mathcal{F},\mathcal{H})$ but as far as I understand that's a different product. Also, what would this 'explicit cofibrant replacement functor' be? Do you perhaps have an example? | |
| Jan 11, 2021 at 19:06 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |