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    • CommentRowNumber1.
    • CommentAuthorMarc Hoyois
    • CommentTimeJul 21st 2013

    Created motivic homotopy theory (renamed from A1-homotopy theory).

    Still many blanks to fill in…

    • CommentRowNumber2.
    • CommentAuthorMarc Hoyois
    • CommentTimeJul 22nd 2013

    I added descriptions of the slice filtration and the 𝔸 1\mathbb{A}^1-Postnikov filtration at motivic homotopy theory.

    • CommentRowNumber3.
    • CommentAuthorMarc Hoyois
    • CommentTimeJul 23rd 2013

    I wrote something about realization functors.

    • CommentRowNumber4.
    • CommentAuthorMarc Hoyois
    • CommentTimeJul 24th 2013

    I wrote something about the six operations.

    • CommentRowNumber5.
    • CommentAuthorMarc Hoyois
    • CommentTimeJul 26th 2013

    I added a few sentences about the relation to the theory of symmetric bilinear forms.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 27th 2013

    Thanks, Marc, for all the work! Glad that you are looking into these nnLab entries on motivic stuff.

    (I’ll read your aditions later, can’t right now…)

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 27th 2013

    Did look at it right now after all. One tiny comment: the link labeled “symmetric space” but pointing to bilinear form should go with a bit more of a comment, since there is also symmetric space.

    • CommentRowNumber8.
    • CommentAuthorMarc Hoyois
    • CommentTimeAug 2nd 2013

    I wrote something about A1-coverings and added the statement of Morel’s connectivity theorem at A1-Postnikov filtration.

    Did look at it right now after all. One tiny comment: the link labeled “symmetric space” but pointing to bilinear form should go with a bit more of a comment, since there is also symmetric space.

    Sorry, I hadn’t noticed. I replaced “symmetric space” with “symmetric bilinear form”.

    • CommentRowNumber9.
    • CommentAuthorMarc Hoyois
    • CommentTimeAug 12th 2013
    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeAug 12th 2013
    • (edited Aug 12th 2013)

    I have added to the entry anchors to the definition of H(S)H(S) and SH(S)SH(S) and cross-links back to these definitions, to make it easier for the reader to jump into the middle of this entry and still know what the notation means.

    • CommentRowNumber11.
    • CommentAuthoradeelkh
    • CommentTimeApr 8th 2014

    I added the reference

    • CommentRowNumber12.
    • CommentAuthoradeelkh
    • CommentTimeDec 27th 2014

    I have moved the subsections on algebraic K-theory and algebraic cobordism to the pages algebraic K-theory spectrum and algebraic cobordism, respectively.

    • CommentRowNumber13.
    • CommentAuthortrent
    • CommentTimeJan 18th 2015
    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeJun 27th 2018

    I thought there was room to state the main definition here (this Def.) more clearly, by saying more explicitly what it means to localize “over a site equipped with an interval”.

    It used to say:

    The motivic homotopy category H(S)\mathrm{H}(S) over SS is the homotopy localization of the (∞,1)-topos of (∞,1)-sheaves on the Nisnevich site Sm/SSm/S equipped with the interval object 𝔸 1\mathbb{A}^1.

    Now I made it say:

    The motivic homotopy category H(S)\mathrm{H}(S) over SS is the homotopy localization at the affine line 𝔸 1\mathbb{A}^1 (1) of the (∞,1)-topos of (∞,1)-sheaves on the Nisnevich site Sm/SSm/S.

    and the link “at the” points to an actual definition of what this means.

    diff, v47, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeJan 7th 2019

    added publication data for

    diff, v50, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeMar 15th 2019
    • (edited Mar 15th 2019)

    added pointer to

    The recording of the second talk will become available later today; will update then.

    diff, v52, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeMar 17th 2019

    added the second recording of Peter Arndt’s talk last week, here

    diff, v53, current

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