List questions from exact-sequence

Published on 26 Feb 2021 - 14:55

302

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Uniqueness of the connecting morphism in the snake lemma

Published on 26 Feb 2021 - 19:51

118

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The connecting morphism of the mapping cone of $\varphi^\bullet$ is $H^i(\varphi^\bullet)$

Published on 27 Feb 2021 - 11:31

44

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Manifold and action associated to a central extension of groups

Published on 30 Mar 2026 - 9:38

343

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How unique is the connecting morphism in the snake lemma?

Published on 02 Mar 2021 - 1:03

65

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Connecting fiber sequences for classifying spaces

Published on 26 Mar 2026 - 7:31

48

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Is the following an example of an exact sequence?

Published on 10 Mar 2021 - 7:43

157

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classifying space of the normalizer of maximal torus and borel construction

Published on 26 Mar 2026 - 7:38

368

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Extensions of $\mathbb{Z}$ by $\mathbb{Z}$

Published on 26 Mar 2026 - 11:06

187

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$\tilde{H}_n(X \cup CA) \simeq H_n(X,A)$

Published on 30 Mar 2026 - 11:22

128

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If $A$ is a deformation retract of $V$ then $H_n(X,A) \simeq H_n(X,V)$

Published on 21 Mar 2021 - 7:43

257

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An example of a module that is not flat.

Published on 27 Mar 2026 - 18:35

75

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if $0 → W → V → V/W → 0$ is a short exact sequence of $\mathfrak{g}$-representations then $B_V = B_{W} + B_{V/W}$

Published on 25 Mar 2021 - 19:38

77

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$X-$ $^T$ $-Y$ $-$ $^S$ $-Z$ is exact then $Z^$ $-$ $^S$ $-Y^$ $-$ $^T$ $-X^*$ is exact.

Published on 27 Mar 2021 - 5:59

75

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Confusion regarding the splitting lemma

Published on 28 Mar 2021 - 2:04

List Question

Why can we assume surjectivity in short exact sequences?

Uniqueness of the connecting morphism in the snake lemma

The connecting morphism of the mapping cone of $\varphi^\bullet$ is $H^i(\varphi^\bullet)$

Manifold and action associated to a central extension of groups

How unique is the connecting morphism in the snake lemma?

Connecting fiber sequences for classifying spaces

Is the following an example of an exact sequence?

classifying space of the normalizer of maximal torus and borel construction

Extensions of $\mathbb{Z}$ by $\mathbb{Z}$

$\tilde{H}_n(X \cup CA) \simeq H_n(X,A)$

If $A$ is a deformation retract of $V$ then $H_n(X,A) \simeq H_n(X,V)$

An example of a module that is not flat.

if $0 → W → V → V/W → 0$ is a short exact sequence of $\mathfrak{g}$-representations then $B_V = B_{W} + B_{V/W}$

$X-$ $^T$ $-Y$ $-$ $^S$ $-Z$ is exact then $Z^$ $-$ $^S$ $-Y^$ $-$ $^T$ $-X^*$ is exact.

Confusion regarding the splitting lemma

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