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nLab > Latest Changes: model structure for orthogonal spectra

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 18th 2016
    • (edited Jun 18th 2016)

    I am working on an entry model structure on orthogonal spectra. So far it contains a detailed construction of the symmetric monoidal strict model structure, and then a detailed proof of the stable model structure.

    (I think its complete, but towards the end the expositional aspects need more polishing, i.e. more cross-links ect. But not today.)

    This follows the writeup that I had started at Model categories of diagram spectra, but (besides being more complete and more polished by now) it works around the issue that I ran into there, by defining the weak equivalences to be the stable weak homotopy equivalences (π *\pi_\ast-isos) right away. This means that the proof still verbatim gives a proof also of the stable model structure on sequential sequential spectra and on excisive functors, but not on symmetric spectra.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 21st 2016

    I think its complete, but towards the end the expositional aspects need more polishing, i.e. more cross-links ect. But not today.

    I have now expanded and polished everything up to and excluding the proof of the stable model structure, hence up to and including this summary remark on the situation for the strict model structure.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 23rd 2016
    • (edited Jun 23rd 2016)

    I think I have found and written out a full proof that the stable model structure on orthogonal spectra is monoidal (here).

    (Couldn’t use the proof offered by MMSS00, due to that caveat)

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 28th 2016

    I have added bunch of further this and that. Now i am writing a Conclusion section summarizing the constructions and theorems.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 29th 2016
    • (edited Jun 29th 2016)

    I have started a section The monoidal stable homotopy category with statement and proof of the tensor triangulated category structure; and then, using that, statement and proof of some basic properties of homotopy commutative ring spectra.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 5th 2016

    I have added a bunch of further stuff to the section Homotopy commutative ring spectra

    • CommentRowNumber7.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 26th 2022
    • (edited Jun 26th 2022)

    This entry is not rendering correctly. The hyperlinked terms do not render at all at the bottom of the page. I was unable to fix this myself.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 27th 2022

    Are you referring to model structure on orthogonal spectra? That renders fine on my machine right now. But it’s a long entry, maybe I am not looking at the relevant bits.

    • CommentRowNumber9.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 27th 2022

    Somebody just edited it today, after I left my previous comment. The problem was corrected by Anonymous.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 27th 2022

    I see. Now I am curious what the problem was. (In the page history one sees no visible change in Anonymous’ edit, and the previous version, rev 87, looks just fine.)

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