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bio website math.berkeley.edu/~aaron
location Berkeley, CA
age 27
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Aug
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comment What are $E_\infty$-rings?
@user40276 -- Right, exactly. (Although you'll actually want (at least) two total of suspensions on your source or loops on your target to deduce that this hom-set is an abelian group.)
Aug
18
comment What are $E_\infty$-rings?
@user40276 Ah, you're pointing out that spectra are all abelian ($\infty$-)group objects? Yes, certainly "$E_\infty$-algebras" in an arbitrary setting needn't be ring-objects in any sense (take the simplest example: sets!), but I think the term "$E_\infty$-ring" only refers to "$E_\infty$-ring spectrum".
Aug
16
comment What are $E_\infty$-rings?
@user40276 -- sorry, I don't quite understand your comment. Could you elaborate? $E_\infty$-rings are commutative monoids in Spectra under the smash product, just as commutative rings are commutative monoids in AbGrp under the tensor product.
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Jul
15
revised What are $E_\infty$-rings?
addendum on dg-algebras, simplicial commutative rings, and E_\infty-ring spectra
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Mar
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comment Refining homotopy commutative maps of spectra to maps of E_{\infty}-ring spectra
The map $MU \to BP$ is a complex orientation, but it's known that it can't be $E$-almost anything. (It's a big open problem whether $BP$ admits an $E_\infty$-structure at all, but even if this exists it won't be compatible with its complex orientation.)
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Feb
27
comment Kan fibrations and surjectivity
Perhaps, if you embed ssets into augmented ssets. Anyways, no matter how you slice it I feel like this is mostly a matter of convention -- although I do like your observation in the comments on the question to which you linked.
Feb
26
comment Kan fibrations and surjectivity
Well, I'd argue that it's certainly defined, exactly as how all the other horns are -- it's just that it's empty!
Dec
30
comment What's the point of spectra?
Thanks Cary! If you work with infinite CW complexes, though, I think this becomes alright again. A phantom map is a nontrivial map which can't be seen by any finite CW complexes.
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