List questions from homological-algebra

46

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Kunneth Theorem for free chain complexes with free cycles and boundaries, over a graded commutative ring

Published on 14 Apr 2026 - 22:59

69

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Let $W=[0,1]\times[0,1]$, where $(0,y)\sim(1,1-y)$ for all $0\leq y\leq 1$. Calculate the homology groups of $W$

Published on 15 Apr 2026 - 15:20

1.1k

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Let $R$ be a Noetherian Ring, then the category of $R$-modules has enough injectives

Published on 11 May 2026 - 1:15

820

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Interpreting a chain map as a double complex (Weibel Exercise 1.2.8)

Published on 15 Apr 2026 - 23:33

380

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The spectral sequence for hyper-derived functors

Published on 13 May 2026 - 16:34

56

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The coface map on Amitsur's complex is an isomorphism.

Published on 11 Apr 2026 - 10:07

431

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Why does group homology do not depend on the coefficient ring?

Published on 10 May 2026 - 14:52

961

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Compact generators in a triangulated category and how they relate to general generators

Published on 13 May 2026 - 13:48

91

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Why is $H_1(N_g)=\mathbb{Z}^{g-1}\oplus\mathbb{Z}_2$?

Published on 10 May 2026 - 16:06

368

Views

Projective limits of compact groups

Published on 11 May 2026 - 1:01

215

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Finite-dimensional irreducible representation with non-vanishing zero weight space

Published on 14 Apr 2026 - 19:33

668

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Is the mapping cone a split complex?

Published on 09 Apr 2026 - 0:55

248

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How to prove this is a triangulated subcategory?

Published on 13 May 2026 - 15:53

395

Views

injective dimension and Ext

Published on 14 May 2026 - 5:33

70

Views

Constructing the cone of a morphism

Published on 08 Apr 2026 - 8:47

List Question

Kunneth Theorem for free chain complexes with free cycles and boundaries, over a graded commutative ring

Let $W=[0,1]\times[0,1]$, where $(0,y)\sim(1,1-y)$ for all $0\leq y\leq 1$. Calculate the homology groups of $W$

Let $R$ be a Noetherian Ring, then the category of $R$-modules has enough injectives

Interpreting a chain map as a double complex (Weibel Exercise 1.2.8)

The spectral sequence for hyper-derived functors

The coface map on Amitsur's complex is an isomorphism.

Why does group homology do not depend on the coefficient ring?

Compact generators in a triangulated category and how they relate to general generators

Why is $H_1(N_g)=\mathbb{Z}^{g-1}\oplus\mathbb{Z}_2$?

Projective limits of compact groups

Finite-dimensional irreducible representation with non-vanishing zero weight space

Is the mapping cone a split complex?

How to prove this is a triangulated subcategory?

injective dimension and Ext

Constructing the cone of a morphism

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