Questions tagged [quasi-isomorphism]
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8 questions
3
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A morphism of double complexes induces a qis on total complexes under certain hypotheses. Proof involving a spectral sequence
$\def\Tot{\operatorname{Tot}}
\def\Ker{\operatorname{Ker}}$I am trying to understand the proof of Lemma 0133 of the Stacks Project. Note that hypotheses (3) and (4) can be restated by saying: extend ...
2
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1
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203
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Left Proper model structure on the category of non-symmetric operads in chain complexes
It is shown in Moriya (Multiplicative formality of operads and
Sinha’s spectral sequence for long knots, 2.1) that there exists a left proper model category structure on non-symmetric operads over $k$-...
- 2,202
4
votes
1
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407
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Homotopy totalization and chains - reference
Simple case. Take $X_{\bullet}$ a cosimplicial space. Is it true that the chain complex of its homotopy totalization is quasi-isomorphic to the homotopy totalization of its chain complex? Because of ...
- 2,202
7
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1
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548
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Induced homeomorphism from a quasi-isometry between hyperbolic spaces
Theorem. Let $\phi:X\rightarrow Y$ be a quasi-isometry between two (Gromov) hyperbolic spaces $X$ and $Y$. If $X$ and $Y$ are proper, then ϕ induces a homeomorphism between their boundaries.
The proof ...
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4
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1
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298
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$A$ is a commutative connective dg-algebra satisfying $H^0(A)=k$. Is it true that a dg ideal generated by elements of negative degree acyclic?
Let $k$ be a field of characteristic zero and $A$ be a graded commutative dg-algebra over $k$ with differential of degree $+1$ satisfying $H^0(A)=k, H^i(A)=0$ for $i<0$. Denote by $\mathcal J$ a dg ...
user21167
2
votes
1
answer
150
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Weakly relatively hyperbolicity and asymptotic cone
Drutu, Sapir, Osin showed that
a finitely generated group $G$ is strongly hyperbolic relative to a finite collection $\mathcal{H}$ of subgroups if and only if any asymptotic cone is tree-graded with ...
- 439
4
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0
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163
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Morphism of distinguished triangles where one of the arrows is a quasi-isomorphism
Let $R$ be any ring and let $A\to B\to C\to [1]$ and $A'\to B'\to C'\to [1]$ be distinguished triangles of complexes of $R$-modules. Let $f:A\to A'$, $g:B\to B'$ and $h:C\to C'$ be morphism of ...
- 1,573
4
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0
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305
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Braided monoidal categories
I know that it has been shown that $E_2$ algebra objects in Categories are simply braided monoidal categories.
In particular, Lurie says that an $E_2$-monoidal structure on the infinity-category $N(C)$...
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