List questions from exact-sequence

Published on 23 Nov 2023 - 23:33

39

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Meaning of projection onto one factor in $0\to A^{r-1}\to A^r\to A\to 0$

Published on 25 Mar 2026 - 7:46

91

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Proving injectivity in a commutative diagram

Published on 27 Nov 2023 - 10:49

148

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A question on diagram of groups

Published on 25 Mar 2026 - 10:54

329

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Suppose $0\to A\to B\to C\to D\to 0$ is exact. Let $0\to A[2]\to B[2]\to C[2]\to X\to 0$ be an exact sequence. Then, $X [2]$ is finite.

Published on 26 Mar 2026 - 8:02

47

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Universal coefficient theorem for a surface groups

Published on 23 Feb 2026 - 3:54

99

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Short exact sequence of Lie Algebra representations

Published on 01 Dec 2023 - 2:59

34

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Prove that the sequence is not convergent

Published on 01 Dec 2023 - 17:04

92

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Is lim^1 trivial when this inverse limit is trivial?

Published on 08 Dec 2023 - 18:34

80

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Direct product implies the splitness of SES.

Published on 09 Dec 2023 - 9:51

71

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Suppose $0\to \Bbb{Z}/2\Bbb{Z}\to A \cong \Bbb{Z}^r\times T\to B\cong \Bbb{Z}^r\times T\to X\to 0$ is an exact sequence.

Published on 10 Dec 2023 - 15:18

43

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$\mathcal{F}$ left-exact functor of abelian categories, then $\mathcal{F}(\ker (f))\cong\ker (\mathcal{F}(f))$

Published on 27 Mar 2026 - 4:35

39

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Short exact sequence with semisimple module in the middle

Published on 18 Dec 2023 - 9:30

50

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Is the first term of this sequence trivial?

Published on 26 Mar 2026 - 22:13

59

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Proof about short exact sequences and Noetherian modules?

Published on 21 Dec 2023 - 23:27

List Question

Which one is the right morphism in the following exact sequence: $0\to A^{r-1}\to A^r\to A\to 0$

Meaning of projection onto one factor in $0\to A^{r-1}\to A^r\to A\to 0$

Proving injectivity in a commutative diagram

A question on diagram of groups

Suppose $0\to A\to B\to C\to D\to 0$ is exact. Let $0\to A[2]\to B[2]\to C[2]\to X\to 0$ be an exact sequence. Then, $X [2]$ is finite.

Universal coefficient theorem for a surface groups

Short exact sequence of Lie Algebra representations

Prove that the sequence is not convergent

Is lim^1 trivial when this inverse limit is trivial?

Direct product implies the splitness of SES.

Suppose $0\to \Bbb{Z}/2\Bbb{Z}\to A \cong \Bbb{Z}^r\times T\to B\cong \Bbb{Z}^r\times T\to X\to 0$ is an exact sequence.

$\mathcal{F}$ left-exact functor of abelian categories, then $\mathcal{F}(\ker (f))\cong\ker (\mathcal{F}(f))$

Short exact sequence with semisimple module in the middle

Is the first term of this sequence trivial?

Proof about short exact sequences and Noetherian modules?

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