Timeline for Examples of rings in monoidal categories
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 22, 2021 at 20:06 | comment | added | Emily | Sorry for taking a while to first reply too! I think maybe this might work more generally: if we consider bicommutative bimonoids in a symmetric monoidal category $\mathcal{C}$ and define bilinear morphisms for them via commutative diagrams (e.g. the requirement $f(1,b)=1$ would look like this), then, as long as $\mathcal{C}$ is sufficiently nice, there should be an associated tensor product $\boxtimes$, defined like in Goerss. Then again the $\boxtimes$-monoids will give ring objects in $\mathsf{CCoMon}(\mathcal{C})$ because of bilinearity (I think) | |
| Jul 21, 2021 at 23:29 | comment | added | Todd Trimble | Sorry to get back late; I've been out of town. Yes, I am regarding bicommutative Hopf algebras as abelian group objects in the category of cocommutative coalgebras, and they are internalizing the usual construction of tensor products of abelian groups. | |
| Jul 18, 2021 at 21:21 | comment | added | Emily | Thanks, Todd! When you refer to the tensor product of bicommutative Hopf algebras, do you mean the one defined (e.g. as) in Theorem 2.1 of arXiv:1804.10153 (coming from Goerss, Prop. 5.5)? | |
| Jul 16, 2021 at 17:38 | history | answered | Todd Trimble | CC BY-SA 4.0 |
