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nLab > Latest Changes: simplicial ring

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 15th 2010
    • (edited Jan 15th 2010)

    added to simplicial ring the definition of the model catgeory structure on modules over simplicial rings.

    I suppose stronger statements are possible, but this I see stated in Toen's lectures and thus briefly noted it down

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 22nd 2015

    I have expanded a little at simplicial ring, making the reflective inclusion of ordinary rings manifest.

    • CommentRowNumber3.
    • CommentAuthorShamrock
    • CommentTimeApr 19th 2024
    It doesn't seem possible that simplicial modules are the tangent infinity category of simplicial commutative rings. At least for an ordinary commutative ring, the fiber is the connective part of the derived category of the ring. This isn't stable because we've thrown away all the coconnective complexes. There are complexes which are not the suspension of anything.
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 19th 2024
    • (edited Apr 19th 2024)

    True, this can’t be right as stated, nor is the Definition-section here the right place to discuss this. I have deleted the line. Thanks for catching this.

    diff, v19, current

1 to 4 of 4

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