List questions from exact-sequence

Published on 05 Jun 2018 - 11:46

115

Views

$0 \rightarrow Q \rightarrow M \rightarrow P \rightarrow 0$ is isomorphic to some $0 \rightarrow N \rightarrow M \rightarrow M/N \longrightarrow 0$

Published on 05 Jun 2018 - 15:00

56

Views

About equivalent formulations of right exact sequences

Published on 25 Mar 2026 - 4:38

88

Views

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

Published on 25 Mar 2026 - 7:47

366

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Isomorphism between two exact sequences

Published on 23 Mar 2026 - 4:16

90

Views

Equality of Hom groups via 5 lemma

Published on 22 Mar 2026 - 7:47

147

Views

Why is a direct summand of a pretriangle a pretriangle?

Published on 17 Mar 2026 - 4:22

158

Views

Conditions on a Module Implied by $\mathrm{Ext}^1 = 0$

Published on 24 Jun 2018 - 5:47

341

Views

Does $V/(\ker f \cap \ker g) \cong \text{im} f +\text{im} g$?

Published on 25 Jun 2018 - 14:31

54

Views

When is the group abelian?

Published on 17 Jul 2018 - 5:28

665

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When a left adjoint functor is exact?

Published on 19 Jul 2018 - 6:18

83

Views

Is it true that $\mathrm{GL}_n(\mathbb{R})=\mathrm{SL}_n(\mathbb{R}) \oplus \{\lambda E : \lambda \in \mathbb{R}^{*}\}$

Published on 25 Mar 2026 - 6:17

657

Views

Projective Resolution of $C[x,y,t]/(x^2+y^2-t)$

Published on 25 Mar 2026 - 1:37

59

Views

Why are additive limit preserving functors left exact?

Published on 13 Aug 2018 - 13:31

166

Views

A question related to group cohomology and spectral sequences

Published on 25 Mar 2026 - 8:11

List Question

Section of a short exact sequence

$0 \rightarrow Q \rightarrow M \rightarrow P \rightarrow 0$ is isomorphic to some $0 \rightarrow N \rightarrow M \rightarrow M/N \longrightarrow 0$

About equivalent formulations of right exact sequences

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

Isomorphism between two exact sequences

Equality of Hom groups via 5 lemma

Why is a direct summand of a pretriangle a pretriangle?

Conditions on a Module Implied by $\mathrm{Ext}^1 = 0$

Does $V/(\ker f \cap \ker g) \cong \text{im} f +\text{im} g$?

When is the group abelian?

When a left adjoint functor is exact?

Is it true that $\mathrm{GL}_n(\mathbb{R})=\mathrm{SL}_n(\mathbb{R}) \oplus \{\lambda E : \lambda \in \mathbb{R}^{*}\}$

Projective Resolution of $C[x,y,t]/(x^2+y^2-t)$

Why are additive limit preserving functors left exact?

A question related to group cohomology and spectral sequences

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