Timeline for What does the Tannakian formalism reconstruct when fed the category of chain complexes?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 27, 2017 at 19:17 | comment | added | მამუკა ჯიბლაძე | So for chain complexes you get certain simplicial Hopf algebra? | |
| Jan 27, 2017 at 16:07 | comment | added | Artur Jackson | Hi. Yes! The theory of cosimplicial schemes certainly arises as Sch($\mathcal{C}$) for the obvious cosmos. I think you are asking how to think of the group valued functors that the theory will spit out? I'll speak generally: one could talk about fpqc group valued sheaves on the one hand, but on the other hand, also saying that an affine algebraic group rel $\mathcal{C}$ is given by a Hopf algebra object in $\mathcal{C}$ is a completely correct description (of affine algebraic groups). There isn't much more happening besides replacing the word algebra many places with 'algebra object,' etc. | |
| Jan 27, 2017 at 5:48 | review | Late answers | |||
| Jan 27, 2017 at 6:33 | |||||
| Jan 27, 2017 at 5:41 | comment | added | მამუკა ჯიბლაძე | Could you explain what is the structure involved in the case of complexes? OK it is something like an algebraic group in the sense of cosimplicial schemes or whatever, but what group? At least "ideologically", could one identify it with something like $\Bbb G_m$, or, say, say what functor from simplicial rings to groups does it represent? | |
| Jan 27, 2017 at 5:32 | history | answered | Artur Jackson | CC BY-SA 3.0 |