List questions from derived-functors

Published on 14 Apr 2026 - 12:40

597

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Does the vanishing of the first derived functor really imply a functor is exact?

Published on 10 Apr 2026 - 23:58

158

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definition of dualizing complex (from Stacks project)

Published on 14 Apr 2026 - 1:53

538

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"Commutativity" of Tor functor

Published on 12 Apr 2026 - 18:00

109

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Derived functor of the realisation in a simplicial model category

Published on 17 Apr 2026 - 1:17

193

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$\mathrm{Ext}^1(N,M)=0$ for all cyclic modules $N$ implies $M$ is injective.

Published on 10 May 2026 - 15:44

172

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Taking stalks and right derived functors of a special type of additive left exact functors

Published on 13 Apr 2026 - 16:44

233

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Proof that Ext Sheaves $\mathscr{Ext}^i _{O_Y}(\mathcal{F}, \mathcal{G})$ are Coherent

Published on 15 Apr 2026 - 3:11

207

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Motivation/intuition behind the definition of delta-functors and related concepts

Published on 12 Apr 2026 - 13:50

88

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Reference request for "higher order" adjoint functors?

Published on 15 Apr 2026 - 3:01

72

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On possible closure operation induced by derived functors

Published on 07 May 2026 - 17:28

16

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how is the target of $\text{tor}_n^R(A,\ )$ related to $\mathbf{Ab}$?

Published on 19 Apr 2026 - 17:35

169

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First Isomorphism Theorem/use

Published on 12 Apr 2026 - 3:04

89

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Characterisation of trivial $n$-extensions

Published on 13 Apr 2026 - 9:52

1k

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Having trouble understanding the Tor functor

Published on 09 Apr 2026 - 4:54

List Question

Derived functor for of a projective module.

Does the vanishing of the first derived functor really imply a functor is exact?

definition of dualizing complex (from Stacks project)

"Commutativity" of Tor functor

Derived functor of the realisation in a simplicial model category

$\mathrm{Ext}^1(N,M)=0$ for all cyclic modules $N$ implies $M$ is injective.

Taking stalks and right derived functors of a special type of additive left exact functors

Proof that Ext Sheaves $\mathscr{Ext}^i _{O_Y}(\mathcal{F}, \mathcal{G})$ are Coherent

Motivation/intuition behind the definition of delta-functors and related concepts

Reference request for "higher order" adjoint functors?

On possible closure operation induced by derived functors

how is the target of $\text{tor}_n^R(A,\ )$ related to $\mathbf{Ab}$?

First Isomorphism Theorem/use

Characterisation of trivial $n$-extensions

Having trouble understanding the Tor functor

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