Aaron Mazel-Gee
Reputation
4,206
Next privilege 5,000 Rep.
Approve tag wiki edits
 Mar27 comment What's the point of spectra? @DmitriPavlov Interesting, thanks for pointing that out! Mar4 awarded Good Answer Jan31 awarded Nice Question Jan12 awarded Good Answer Oct31 awarded Popular Question Sep30 awarded Explainer Sep27 awarded Yearling Sep13 awarded Good Question Aug20 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.) Aug18 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". Aug16 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. Aug2 awarded Nice Question Jul15 revised What are $E_\infty$-rings? addendum on dg-algebras, simplicial commutative rings, and E_\infty-ring spectra Jul2 awarded Curious Apr2 awarded Popular Question Mar23 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.) Mar11 awarded Popular Question Feb27 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. Feb26 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! Dec30 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.