Timeline for What structure on a monoidal category would make its 2-category of module categories monoidal and braided?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 8, 2009 at 22:44 | vote | accept | Ben Webster♦ | ||
| Dec 8, 2009 at 22:44 | history | bounty ended | Ben Webster♦ | ||
| Dec 7, 2009 at 15:31 | history | edited | Chris Schommer-Pries | CC BY-SA 2.5 |
fixed terminology
|
| Dec 7, 2009 at 15:12 | comment | added | David Jordan | Somehow, I hadn't heard of these Hopfish algebras before, even though it's a very natural thing to do. Thanks for the references! | |
| Dec 7, 2009 at 14:56 | comment | added | Chris Schommer-Pries | Yes. That's exactly right. (Your expression didn't come out, but I know what you mean). There is a "pentagonator". The relevant diagrams are precisely those used to define a tricategory, so can be seen for example in the paper by Gordan-Powers-Street on that subject. Btw, a similar statement holds for algebras. If you have an $A - A\otimes A$ bimodule (and counit which satisfies the pentagon and triangle axioms) then you get an induced monoidal structure on A-Mod. If you add an antipode then these go under the name "Hopfish" algebras. I think this concept is due to Alan Weinstein. | |
| Dec 7, 2009 at 14:41 | comment | added | David Jordan | This seems like a good point, about replacing functors with bimodule categories. What does one write about co-associativity? Perhaps there should be an equivalence $\alpha$ of bimodule categories between the two different coproduct expressions $(\Delta \ot \id)\circ\Delta$ and $(\id\ot\Delta)\circ \Delta$, which would satisfy the pentagon axiom only up to natural isomorphism of functors, something like this? | |
| Dec 7, 2009 at 13:16 | history | answered | Chris Schommer-Pries | CC BY-SA 2.5 |