List questions from exact-sequence

Published on 24 May 2015 - 3:29

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$\mathbb{Q}$ is a flat $\mathbb{Z}$-module

Published on 26 Mar 2026 - 17:29

404

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$M_1 \to M_2 \to M_3 \to 0$ exact iff $0 \to \text{Hom}_A(M_3, N) \to \text{Hom}_A(M_2, N) \to \text{Hom}_A(M_1, N)$ is exact.

Published on 27 May 2015 - 21:57

556

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Understanding splitting lemma

Published on 09 Jun 2015 - 2:35

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Flat modules and their relationship with short exact sequences

Published on 26 Mar 2026 - 18:58

302

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Exact sequence of vector bundles

Published on 28 Mar 2026 - 5:58

632

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Where is sheafification in the definition of exact sequence of sheaves?

Published on 13 Jun 2015 - 7:04

537

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Diagram with exact sequences of modules

Published on 18 Jun 2015 - 13:09

609

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Do we have a "short five lemma" for any two of the isomorphisms?

Published on 28 Jun 2015 - 21:32

115

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Show that every short exact sequence $0\rightarrow M' \rightarrow M \rightarrow M'' \rightarrow 0$ (with $M''$ free) is split exact

Published on 30 Jun 2015 - 11:43

80

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Analysing Exact Sequence

Published on 28 Mar 2026 - 8:28

131

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How to choose a left-add$(X)$-approximation with a certain property

Published on 02 Jul 2015 - 17:21

387

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Prove that there's a unique morphism that completes the commutative diagram

Published on 25 Mar 2026 - 12:29

772

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Exact sequences of projective modules

Published on 29 Mar 2026 - 6:30

210

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short exact sequence of algebras over a field

Published on 11 Jul 2015 - 1:55

List Question

A short exact sequence + exact sequence of opposite direction = split?

$\mathbb{Q}$ is a flat $\mathbb{Z}$-module

$M_1 \to M_2 \to M_3 \to 0$ exact iff $0 \to \text{Hom}_A(M_3, N) \to \text{Hom}_A(M_2, N) \to \text{Hom}_A(M_1, N)$ is exact.

Understanding splitting lemma

Flat modules and their relationship with short exact sequences

Exact sequence of vector bundles

Where is sheafification in the definition of exact sequence of sheaves?

Diagram with exact sequences of modules

Do we have a "short five lemma" for any two of the isomorphisms?

Show that every short exact sequence $0\rightarrow M' \rightarrow M \rightarrow M'' \rightarrow 0$ (with $M''$ free) is split exact

Analysing Exact Sequence

How to choose a left-add$(X)$-approximation with a certain property

Prove that there's a unique morphism that completes the commutative diagram

Exact sequences of projective modules

short exact sequence of algebras over a field

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