User Marc Hoyois

40 votes

Accepted

Is the fundamental group functor a left-adjoint?

answered Oct 16, 2012 at 4:42

29 votes

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Voevodsky's six functor formalism VS Lucas Mann's

answered Feb 13, 2023 at 22:11

25 votes

Why is the motivic category defined over the site of smooth schemes only?

answered Jan 4, 2018 at 22:53

22 votes

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When is a topological space the homotopy colimit of an open covering?

answered Nov 23, 2014 at 17:31

19 votes

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Which limits commute with filtered colimits in the category of sets?

answered Aug 22, 2013 at 21:48

18 votes

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Category of motivic spectra

answered Oct 19, 2013 at 1:10

18 votes

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Is the $\infty$-topos $Sh(X)$ hypercomplete whenever $X$ is a CW complex?

answered Aug 8, 2016 at 11:58

16 votes

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$BG$ the stack, $BG$ the simplicial presheaf

answered Oct 18, 2018 at 15:24

16 votes

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Does the forgetful functor from presentable $\infty$-categories to $\infty$-categories preserve filtered colimits?

answered Jul 5, 2015 at 10:03

16 votes

Can we define homotopy groups using Tannakian categories

answered Mar 24, 2012 at 17:25

15 votes

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Sheaves of complexes and complexes of sheaves

answered Mar 26, 2017 at 21:03

15 votes

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Who proved the motivic 6-functor formalism?

answered Feb 8 at 21:28

14 votes

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Perfect chain complexes

answered Sep 8, 2016 at 1:41

14 votes

What's with equivariant homotopy theory over a compact Lie group?

answered Sep 1, 2017 at 4:31

14 votes

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The vanishing of $MGL^{2n+i,n}(X)$; do spectra of smooth projective varieties generate $SH_{l}$?

answered Nov 11, 2012 at 7:05

14 votes

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Is the site of (smooth) manifolds hypercomplete?

answered May 18, 2013 at 10:15

14 votes

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Diffeology as a sheaf on the site of smooth manifolds

answered Jul 26, 2013 at 18:45

13 votes

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Tensor products of $\mathbb{E}_\infty$-spaces

answered Aug 7, 2021 at 20:53

13 votes

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If we replace the spectrally ringed space in the definition of a spectral scheme with an arbitrary infinity-topos, what objects do we get?

answered Apr 22, 2022 at 6:05

13 votes

What is the dual of the stable infinity category of perfect complex on smooth proper variety?

answered Jul 28, 2022 at 5:44

13 votes

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Realization Functor From $SH$ to Derived Category of $Gal$-Modules

answered Nov 21, 2015 at 1:16

13 votes

What is the negative cyclic homology of a smooth projective variety?

answered Nov 18, 2016 at 16:18

12 votes

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Are there continua in $\infty$-topoi?

answered Oct 9, 2018 at 1:13

11 votes

Determinantal identities for perfect complexes

answered Sep 7, 2020 at 17:53

11 votes

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How duality follows from a six functor formalism

answered Sep 25, 2021 at 7:31

11 votes

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Derived version of equivalence between motives and representations of Motivic galois groups?

answered Nov 10, 2016 at 18:09

11 votes

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Example of a locally presentable locally cartesian closed category which is not a topos?

answered Feb 28, 2018 at 5:40

11 votes

motivic t-structure and realisations

answered Sep 20, 2012 at 23:18

11 votes

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A Kunneth formula for the etale cohomology of the product of ('simple') varieties over not (necessarily) algebraically closed field

answered Mar 4, 2012 at 21:52

10 votes

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Homotopy left-exactness of a left derived functor

answered May 23, 2013 at 19:05

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82 Answers

Is the fundamental group functor a left-adjoint?

Voevodsky's six functor formalism VS Lucas Mann's

Why is the motivic category defined over the site of smooth schemes only?

When is a topological space the homotopy colimit of an open covering?

Which limits commute with filtered colimits in the category of sets?

Category of motivic spectra

Is the $\infty$-topos $Sh(X)$ hypercomplete whenever $X$ is a CW complex?

$BG$ the stack, $BG$ the simplicial presheaf

Does the forgetful functor from presentable $\infty$-categories to $\infty$-categories preserve filtered colimits?

Can we define homotopy groups using Tannakian categories

Sheaves of complexes and complexes of sheaves

Who proved the motivic 6-functor formalism?

Perfect chain complexes

What's with equivariant homotopy theory over a compact Lie group?

The vanishing of $MGL^{2n+i,n}(X)$; do spectra of smooth projective varieties generate $SH_{l}$?

Is the site of (smooth) manifolds hypercomplete?

Diffeology as a sheaf on the site of smooth manifolds

Tensor products of $\mathbb{E}_\infty$-spaces

If we replace the spectrally ringed space in the definition of a spectral scheme with an arbitrary infinity-topos, what objects do we get?

What is the dual of the stable infinity category of perfect complex on smooth proper variety?

Realization Functor From $SH$ to Derived Category of $Gal$-Modules

What is the negative cyclic homology of a smooth projective variety?

Are there continua in $\infty$-topoi?

Determinantal identities for perfect complexes

How duality follows from a six functor formalism

Derived version of equivalence between motives and representations of Motivic galois groups?

Example of a locally presentable locally cartesian closed category which is not a topos?

motivic t-structure and realisations

A Kunneth formula for the etale cohomology of the product of ('simple') varieties over not (necessarily) algebraically closed field

Homotopy left-exactness of a left derived functor