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Bryan Shih
Bryan Shih
4:22 PM
Hi all, i'm wondering if what we can say about what kind of limits the inclusion of connective spectra to general spectra, Sp_{\ge 0} \hookrightarrow Sp. commute with. For example, pullbacks.

(why i'm interested : In line 2,p2 of the following paper, https://arxiv.org/pdf/1808.05559.pdf
It seems to imply that an ordinary pb square of assoc. rings is also a pb when regarded as E_1 ring spectra. )
 
William Balderrama
William Balderrama
@BryanShih The recipe for computing a limit of a diagram in connective spectra is: compute the limit in spectra, then take the connective cover. In particular, the limit is preserved by the inclusion Sp^cn -> Sp if and only if the limit taken in Sp is already connective.
In your example this relies on the assumption that B -> B' is surjective.
 
Bryan Shih
Bryan Shih
@WilliamBalderrama perfect, thannks!
 

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