Timeline for Fiber product of group rings
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 3, 2021 at 21:10 | comment | added | R. van Dobben de Bruyn | One possible way to prove something like this is if the free functor $F \colon \mathbf{Gp} \to \mathbf{Hopf}_K$ has a left adjoint. It does have a right adjoint given by grouplike elements, but I have no idea if it has a left adjoint (this would imply much more limits commute, which is maybe too optimistic). | |
| Jun 3, 2021 at 20:15 | comment | added | Benjamin Steinberg | It seems the tensor product is the product so I withdraw my objection. | |
| Jun 3, 2021 at 20:06 | comment | added | Benjamin Steinberg | @R.vanDobbendeBruyn sorry I hadn't caught that it was taken in hopf algebras. That's out of my pay grade | |
| Jun 3, 2021 at 20:02 | comment | added | R. van Dobben de Bruyn | @BenjaminSteinberg is the product in Hopf algebras really just the direct product? I can't think of a natural comultiplication on that. (Analogously, in the commutative case, the coproduct in affine group schemes is not given by disjoint union, as the latter does not have a natural group structure.) | |
| Jun 3, 2021 at 19:45 | comment | added | Benjamin Steinberg | This seems false. If G is trivial, on the left side you have the tensor product of group rings and in the right the direct product | |
| Jun 3, 2021 at 17:52 | history | asked | Hadrian Heine | CC BY-SA 4.0 |