List questions from exact-sequence

Published on 30 Nov 2022 - 20:45

80

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For every exact sequence $0 \to N \xrightarrow{f} M \xrightarrow{g} L \to 0$ the following are equivalent

Published on 04 Dec 2022 - 2:52

122

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Lie algebra-Lie group correspondence of an exact sequence

Published on 07 Dec 2022 - 9:29

129

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On a non split exact sequence

Published on 07 Dec 2022 - 17:02

129

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If a short exact sequence ends in a free module, then it admits a section

Published on 30 Mar 2026 - 2:30

96

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On exact sequences of finite-dimensional inner product spaces

Published on 13 Dec 2022 - 12:15

88

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Example of calculating $\text{Tor}_1(M,N)$ for modules $M$ and $N$

Published on 14 Dec 2022 - 20:18

55

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Showing that there is no Left splitting in the following exact sequence of groups.

Published on 19 Dec 2022 - 19:05

188

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Proving that a sequence is exact and non-split

Published on 22 Dec 2022 - 1:55

121

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Problem 2.2 Atiya and MacDonald pg.31

Published on 22 Dec 2022 - 2:28

63

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Proving that another sequence is exact and non-split (Correcting the function $p$ to make it exact)

Published on 22 Dec 2022 - 16:09

128

Views

What does it mean for the tensor functor to be right exact?

Published on 22 Dec 2022 - 16:31

120

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Exact sequence with reduced homology

Published on 22 Dec 2022 - 18:44

79

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Equivalent definitions of left exact functors

Published on 29 Mar 2026 - 10:27

147

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Sheaf cohomology of Hopf surface.

Published on 29 Mar 2026 - 14:31

List Question

Analogue of Module Sum in an Exact Category

For every exact sequence $0 \to N \xrightarrow{f} M \xrightarrow{g} L \to 0$ the following are equivalent

Lie algebra-Lie group correspondence of an exact sequence

On a non split exact sequence

If a short exact sequence ends in a free module, then it admits a section

On exact sequences of finite-dimensional inner product spaces

Example of calculating $\text{Tor}_1(M,N)$ for modules $M$ and $N$

Showing that there is no Left splitting in the following exact sequence of groups.

Proving that a sequence is exact and non-split

Problem 2.2 Atiya and MacDonald pg.31

Proving that another sequence is exact and non-split (Correcting the function $p$ to make it exact)

What does it mean for the tensor functor to be right exact?

Exact sequence with reduced homology

Equivalent definitions of left exact functors

Sheaf cohomology of Hopf surface.

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