List questions from homological-algebra

Published on 05 Jul 2019 - 20:16

535

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"Commutativity" of Tor functor

Published on 25 Mar 2026 - 9:24

534

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Derived proofs of elementary homological algebra theorems?

Published on 25 Mar 2026 - 13:05

53

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Image of induced homomorphisms, with different differentials

Published on 09 Jul 2019 - 6:29

245

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Stalk of the product or power of quasi-coherent ideal sheaves

Published on 25 Mar 2026 - 14:25

299

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Chain homotopy of Cartan-Eilenberg resolutions induced by homotopic maps of chain complexes

Published on 27 Mar 2026 - 4:21

150

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Is the boundary map generated by zig-zag lemma a homomorphism between modules?

Published on 14 Jul 2019 - 18:43

38

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Give an example of cochain maps?

Published on 16 Jul 2019 - 13:06

110

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Give an example of cochain map which is bijective?

Published on 16 Jul 2019 - 13:26

76

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Isomorphism between Topological Groups.

Published on 25 Mar 2026 - 4:34

56

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Counit of This Adjunction in Andre-Quillen Cohomology (Abelianization Functor)

Published on 23 Jul 2019 - 0:18

49

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$\mathrm{Ext}_{S}^{m}(S \otimes_{R} M,N)\cong \mathrm{Ext}_{R}^{m}(M,N)$

Published on 23 Jul 2019 - 13:02

43

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making sense of hom-set between chain complex and abelian group

Published on 23 Jul 2019 - 13:49

190

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$\mathrm{Ext}^1(N,M)=0$ for all cyclic modules $N$ implies $M$ is injective.

Published on 25 Mar 2026 - 9:24

127

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Showing that $R \otimes_{R[X]} R[Y] \cong R[Y]/(Y^2)$

Published on 24 Jul 2019 - 18:18

List Question

Zero map between spectral sequences

"Commutativity" of Tor functor

Derived proofs of elementary homological algebra theorems?

Image of induced homomorphisms, with different differentials

Stalk of the product or power of quasi-coherent ideal sheaves

Chain homotopy of Cartan-Eilenberg resolutions induced by homotopic maps of chain complexes

Is the boundary map generated by zig-zag lemma a homomorphism between modules?

Give an example of cochain maps?

Give an example of cochain map which is bijective?

Isomorphism between Topological Groups.

Counit of This Adjunction in Andre-Quillen Cohomology (Abelianization Functor)

$\mathrm{Ext}_{S}^{m}(S \otimes_{R} M,N)\cong \mathrm{Ext}_{R}^{m}(M,N)$

making sense of hom-set between chain complex and abelian group

$\mathrm{Ext}^1(N,M)=0$ for all cyclic modules $N$ implies $M$ is injective.

Showing that $R \otimes_{R[X]} R[Y] \cong R[Y]/(Y^2)$

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