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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• 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 $\mathbb{A}^1$-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 $n$Lab entries on motivic stuff.

• 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 $H(S)$ and $SH(S)$ 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.
• CommentTimeApr 8th 2014

• CommentRowNumber12.
• 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 $\mathrm{H}(S)$ over $S$ is the homotopy localization of the (∞,1)-topos of (∞,1)-sheaves on the Nisnevich site $Sm/S$ equipped with the interval object $\mathbb{A}^1$.

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

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

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeJan 7th 2019

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

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

• CommentRowNumber17.
• CommentAuthorUrs
• CommentTime7 days ago

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