List questions from exact-sequence

Published on 28 Mar 2021 - 12:54

481

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Taking $G$-invariants over a short exact sequence of $G$-modules

Published on 03 Apr 2021 - 0:19

1.2k

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Understanding the Euler sequence on $\mathbb{P}^n$

Published on 04 Apr 2021 - 10:26

86

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Is that a exact sequence?

Published on 09 Apr 2021 - 4:07

136

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Why doesn't right exactness of a functor (say tensor product) imply exact?

Published on 28 Mar 2026 - 5:22

1k

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Understanding short exact sequences

Published on 11 Apr 2021 - 5:23

99

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Question about commutative diagram

Published on 11 Apr 2021 - 15:27

134

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What is the right derived functor of $\lim_\leftarrow$?

Published on 28 Mar 2026 - 5:22

266

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Definition of $\tilde{H}_n(X,A)$

Published on 25 Mar 2026 - 20:11

730

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Specific proof that the pullback of quasi-coherent sheaf is quasi-coherent

Published on 26 Mar 2026 - 21:27

104

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What is a simple example for an exact sequence? Because in my opinion it seems that all the modules in the sequence should be equal to zero

Published on 17 Apr 2021 - 22:47

75

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Prove that the map is injective if the rows and the columns are exact in the commutative diagram (self-ansered).

Published on 18 Apr 2021 - 16:04

77

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$0 \longrightarrow C(A)\otimes C(Y) + C(X)\otimes C(B) \longrightarrow C(X)\otimes C(Y) \longrightarrow C(X,A)\otimes C(Y,B) \longrightarrow 0$

Published on 21 Apr 2021 - 21:48

29

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Subgroups of abelian-by-abelian groups

Published on 22 Apr 2021 - 8:39

145

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Commutativity of a diagram involving extension of scalars

Published on 27 Mar 2026 - 18:27

List Question

how the Snake Lemma has been applied here?

Taking $G$-invariants over a short exact sequence of $G$-modules

Understanding the Euler sequence on $\mathbb{P}^n$

Is that a exact sequence?

Why doesn't right exactness of a functor (say tensor product) imply exact?

Understanding short exact sequences

Question about commutative diagram

What is the right derived functor of $\lim_\leftarrow$?

Definition of $\tilde{H}_n(X,A)$

Specific proof that the pullback of quasi-coherent sheaf is quasi-coherent

What is a simple example for an exact sequence? Because in my opinion it seems that all the modules in the sequence should be equal to zero

Prove that the map is injective if the rows and the columns are exact in the commutative diagram (self-ansered).

$0 \longrightarrow C(A)\otimes C(Y) + C(X)\otimes C(B) \longrightarrow C(X)\otimes C(Y) \longrightarrow C(X,A)\otimes C(Y,B) \longrightarrow 0$

Subgroups of abelian-by-abelian groups

Commutativity of a diagram involving extension of scalars

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