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Results tagged with homological-algebra
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user 82627
(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.
1
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Accepted
Why is the flat cotorsion pair actually a cotorsion pair?
The category of sheaves on a ringed space is a Grothendieck category. Let $Q$ denote an injective cogenerator. We write $hom$ for internal and $Hom$ for external hom.
Let $F^+:=hom(F,Q)$. Then for an …
- 501
1
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2
answers
201
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Why is the flat cotorsion pair actually a cotorsion pair?
I asked this question some while ago on Stack Exchange but didn't get an answer (link), so I am trying it here as well.
Fix a ringed space $(X,\mathcal{O})$ and denote by $\mathcal{F}$ the class of f …
- 501
6
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0
answers
241
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Flat Model Structure on $\mathbf{Ch}(\mathbf{Mod}(\mathcal{O}_X))$ computes pullback / pushf...
Given a ringed space $(X,\mathcal{O})$ of can construct the flat model structure on chain complexes of $\mathcal{O}$-modules:
Weak equivalences are quasi-isomorphisms
The fibrations are epimorphisms …
- 501
3
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0
answers
209
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Landweber Exact Functor Theorem for Cohomology
I have seen the Landweber exact functor theorem beeing used to retrieve cohomology theories, in particular singular cohomology and K-Theory.
However the statement of the theorem itself is always homol …
- 501
5
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answers
267
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K-flat, K-flabby resolution
Let $X$ be a topological space and $F$ a flat sheaf of abelian groups. It is well known that taking the Godement resolution of $F$ gives rise to a "flabbyflat" or "flasqueflat" resolution, in the sens …
- 501
3
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0
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151
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Derived base change of (nice) topological spaces
Let $f:X\to Y$ be a morphism of (nice) topological spaces. consider the basechange along $g:Y'\to Y$. We write $F:X'\to Y'$ and $G:X'\to X$.
Consider some class of sheaves on those spaces, e.g. abeli …
- 501