Timeline for Duality of Hopf algebras and duality of spectra
Current License: CC BY-SA 4.0
6 events
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| Nov 19, 2019 at 18:30 | history | edited | Dmitry Vaintrob | CC BY-SA 4.0 |
got rid of faithfulness statement in exposition (couldn't find reference)
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| Nov 19, 2019 at 18:25 | comment | added | Dmitry Vaintrob | I looked and couldn't find the reference, so I might be wrong about this faithfulness result. Since the question doesn't depend on it, I'll edit it out... | |
| Nov 19, 2019 at 18:22 | comment | added | Dmitry Vaintrob | @GeoffroyHorel by loop spectrum of $X$ I mean $\Omega^\infty \Sigma^\infty(X)$. You're right and I was wrong that Mandel's result is about cochains with prime coefficients. Thank you also for linking Allen's article, which I didn't know about. But both of these are results about reconstruction of a space from Eilenberg-McLane cohomology theories. What I was referring to (and seem to remember hearing somewhere) is that the assignment $X\mapsto S(X)$ is fully faithful without any Frobenius, with the partial inverse $E\mapsto Hom(E, S)$ (hom space in the category of $E_\infty$ algebras). | |
| Nov 19, 2019 at 12:15 | comment | added | Geoffroy Horel | What do you mean by free loop spectrum ? From the rest of what you wrote I understand that $S(X)$ is the mapping spectrum from the infinite suspension of $X$ to the sphere spectrum. But I don't think that this functor is fully faithful when you view it as a functor to $E_\infty$-algebras, you need to add some extra structure to your $E_\infty$-algebras (see the following recent preprint : arxiv.org/abs/1910.00999) | |
| Nov 17, 2019 at 20:45 | history | edited | Dmitry Vaintrob | CC BY-SA 4.0 |
added 8 characters in body; edited tags
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| Nov 17, 2019 at 20:31 | history | asked | Dmitry Vaintrob | CC BY-SA 4.0 |