Timeline for Tensor products of $\infty$-algebras over operads
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2019 at 15:42 | comment | added | QcH | @TheoJohnson-Freyd Do you mind sharing the formula in terms of "sums over diagrams" mentioned at the end of your answer? A reference would also be great! Thanks! | |
| Feb 6, 2018 at 21:59 | comment | added | Theo Johnson-Freyd | @DanPetersen Could be. I only understand things in characteristic zero. | |
| Feb 5, 2018 at 19:10 | comment | added | Dan Petersen | @Theo Both maps are quasi-isomorphisms in general - I think you mean that neither $L_\infty$ nor $C_\infty$ are cofibrant. | |
| Feb 5, 2018 at 17:55 | comment | added | Theo Johnson-Freyd | @DanPetersen I only understand things in characteristic zero. I could be mistaken, but I believe that in non-zero characteristic, neither map $C_\infty \to C$ nor $L_\infty\to L$ is a quasiisomorphism. | |
| Feb 5, 2018 at 17:54 | comment | added | Theo Johnson-Freyd | @PavelSafronov You know this literature much better than I do, so I trust your namings. I have certainly seen the name "Boardman--Vogt tensor product" used for the operation on dg operads given by $(A\otimes B)(n) = A(n) \otimes B(n)$. This is the monoidal structure that I mean. | |
| Feb 4, 2018 at 21:57 | comment | added | Fernando Muro | @DanPetersen I think that even $L_\infty$-algebras only work in characteristic 0. | |
| Feb 4, 2018 at 18:20 | comment | added | Pavel Safronov | When you say the Boardman--Vogt tensor product, do you really mean the Hadamard tensor product? Is there a definition of the BV tensor product for operads in a non-Cartesian monoidal category? | |
| Feb 4, 2018 at 17:42 | comment | added | Dan Petersen | Thanks! This only works over a field of characteristic zero, right? If there were a sum over trees formula, one could hope to verify the statement over the integers. | |
| Feb 4, 2018 at 17:24 | history | answered | Theo Johnson-Freyd | CC BY-SA 3.0 |