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nLab: Properties of the functor giving spectral sequences of filtered objects

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  1. In this page https://ncatlab.org/nlab/show/spectral+sequence+of+a+filtered+stable+homotopy+type there is a big pink rectangle with a theorem.

    I'm wondering what properties does the functor there have. In particular, I'm intrigued about additional structure on the spectral sequence coming from additional structure on the filtration, like e.g. in the spectral sequence of a filtered complex, if the complex is an algebra and the filtration is of algebras, then the spectral sequence is multiplicative. This naively seems to me like saying that this functor is (symmetric) lax monoidal when we are in presence of additional monoidal structure, etc. I know this is vague, I just wanted to know if this sounds reasonable or if it has appeared somewhere. Thanks!
    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 13th 2016

    If you write [[spectral sequence of a filtered stable homotopy type]] when you post here, then you get this spectral sequence of a filtered stable homotopy type.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 13th 2016

    I just wanted to know if this sounds reasonable

    Yes, it does.

    or if it has appeared somewhere.

    Not that I knew of.

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