List questions from homological-algebra

Published on 26 Mar 2026 - 6:25

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Calculate $\text{Ext}_{\mathbb{Z}}^1(\mathbb{Q}/\mathbb{Z}, \mathbb{Z}) $?

Published on 29 Mar 2018 - 3:07

397

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Calculate the Pontragin dual $\text{Hom}_{\mathbb{Z}}(\mathbb{Q}/\mathbb{Z}, \mathbb{Q}/\mathbb{Z})$.

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Subquotients of Module

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910

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Any exact sequence of injective objects splits

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693

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Questions on hypercohomology

Published on 22 Mar 2026 - 0:08

452

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DGA formality via $A_\infty$

Published on 03 Apr 2018 - 7:29

173

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First page of a spectral sequence

Published on 23 Mar 2026 - 7:35

698

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Short exact sequence of functors which splits, but not naturally (revisited, motivated by the Universal Coefficient Theorem)

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233

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Derived functor defined with an adapted subcategory

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68

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In an abelian category, we have a commutative square if and only if the composition through the direct sum is zero

Published on 05 Apr 2018 - 23:46

2.6k

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Extension group and Baer sum

Published on 26 Mar 2026 - 12:05

163

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(Co)homology of a closed 4-manifold with $\mathbb{Z}/p$ coefficients

Published on 06 Apr 2018 - 16:15

110

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Show that, if $u: B \rightarrow C$ and $v:D \rightarrow E$ are cochain maps, then $vfu$ and $vgu$ are chain homotopic.

Published on 06 Apr 2018 - 17:38

101

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Regarding the chain complexes of semisimplicial sets

Published on 25 Mar 2026 - 17:18

List Question

Homology with real coefficients

Calculate $\text{Ext}_{\mathbb{Z}}^1(\mathbb{Q}/\mathbb{Z}, \mathbb{Z}) $?

Calculate the Pontragin dual $\text{Hom}_{\mathbb{Z}}(\mathbb{Q}/\mathbb{Z}, \mathbb{Q}/\mathbb{Z})$.

Subquotients of Module

Any exact sequence of injective objects splits

Questions on hypercohomology

DGA formality via $A_\infty$

First page of a spectral sequence

Short exact sequence of functors which splits, but not naturally (revisited, motivated by the Universal Coefficient Theorem)

Derived functor defined with an adapted subcategory

In an abelian category, we have a commutative square if and only if the composition through the direct sum is zero

Extension group and Baer sum

(Co)homology of a closed 4-manifold with $\mathbb{Z}/p$ coefficients

Show that, if $u: B \rightarrow C$ and $v:D \rightarrow E$ are cochain maps, then $vfu$ and $vgu$ are chain homotopic.

Regarding the chain complexes of semisimplicial sets

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