List questions from homological-algebra

Published on 27 Mar 2026 - 1:00

158

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Why is a DG-enhancement of the derived bounded category of coherent sheaves an enhancement?

Published on 04 Apr 2026 - 11:46

620

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Introductory book for homological algebra

Published on 16 Apr 2020 - 20:34

120

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Show that if $N$ is connected non-compact, orientable n-dimensional manifold, then $H_{n}(N; \mathbb{Z}) = 0.$

Published on 23 Feb 2026 - 2:59

414

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Naturality of the ker-coker sequence of snake lemma in an abelian category

Published on 02 Apr 2026 - 23:15

257

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Example of a pre-abelian category but not a semi-abelian category?

Published on 18 Apr 2020 - 3:33

142

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Kan extensions and satellite functors

Published on 25 Mar 2026 - 14:02

271

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Why Grothendieck group of an Abelian category is well-defined?

Published on 19 Apr 2020 - 5:59

92

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Short exact sequences envolving syzygies

Published on 27 Mar 2026 - 10:15

42

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If $0\stackrel{f}\rightarrow V \stackrel{g}\rightarrow 0$ is an exact sequence, then $V = 0$.

Published on 27 Mar 2026 - 10:15

272

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Determine the cohomology ring $H^*(\mathbb{R}P^n; \mathbb{Z}).$

Published on 27 Mar 2026 - 0:57

177

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Is it true that an arbitrary coproduct of compact objects is compact?

Published on 21 Apr 2020 - 15:58

362

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Graded tensor product of rings in Künneth formula

Published on 21 Apr 2020 - 16:29

856

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External power of locally free sheaves

Published on 27 Mar 2026 - 10:10

367

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Show that every map of $S^{k + l} \rightarrow S^k \times S^l$ induces the given trivial homomorphism.

Published on 25 Mar 2026 - 19:07

List Question

Cohomology/Homology of $\mathbb{Z}[1/p]$

Why is a DG-enhancement of the derived bounded category of coherent sheaves an enhancement?

Introductory book for homological algebra

Show that if $N$ is connected non-compact, orientable n-dimensional manifold, then $H_{n}(N; \mathbb{Z}) = 0.$

Naturality of the ker-coker sequence of snake lemma in an abelian category

Example of a pre-abelian category but not a semi-abelian category?

Kan extensions and satellite functors

Why Grothendieck group of an Abelian category is well-defined?

Short exact sequences envolving syzygies

If $0\stackrel{f}\rightarrow V \stackrel{g}\rightarrow 0$ is an exact sequence, then $V = 0$.

Determine the cohomology ring $H^*(\mathbb{R}P^n; \mathbb{Z}).$

Is it true that an arbitrary coproduct of compact objects is compact?

Graded tensor product of rings in Künneth formula

External power of locally free sheaves

Show that every map of $S^{k + l} \rightarrow S^k \times S^l$ induces the given trivial homomorphism.

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