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Results tagged with homological-algebra
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user 112348
(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.
11
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If C is a cocomplete coalgebra, then $\psi:C\rightarrow B\Omega C$ is a filtered quasi-isomo...
I am reading the PhD thesis thesis of Kenji Lefèvre-Hasegawa and the corresponding errata by Bernhard Keller, my question is about the first error found in the thesis. Lemma 1.3.2.3 c states 'the adju …
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5
votes
0
answers
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Does the associated graded functor take products of filtered k-coalgebras to graded k-coalge...
Let's suppose we have two noncommutative graded k-coalgebras $C_1$ and $C_2$ with respective admissible filtrations (i.e $F_{0}C_i=0$ and $\mathrm{colim}_k F_kC_i=C_i$), I would like to know if there …
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3
votes
2
answers
187
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Two definitions of minimal models
Is there any relationship between both definitions of minimal models? (the couple of definitions I know are the one mentioned in Lefèvre's thesis, in the sense that the differential is zero, and the o …
- 795
1
vote
If C is a cocomplete coalgebra, then $\psi:C\rightarrow B\Omega C$ is a filtered quasi-isomo...
If $\mathrm{Gr}(B\Omega C)\xrightarrow{\backsim} B\Omega(\mathrm{Gr} C)$ actually means they both are not isomorphic but there is a canonical quasi-isomorphism from $\mathrm{Gr}(B\Omega C)$ to $B\Ome …
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