Question

Example of a factorisation of functors $F = HK$ for which the Kan extension of $F$ along $K$ is not $H$.

score 39 · Answer 1 · 2023-10-28 14:39:15

39

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Example of a factorisation of functors $F = HK$ for which the Kan extension of $F$ along $K$ is not $H$.

Published on 28 Oct 2023 - 14:39

score 29 · Answer 2 · 2023-11-04 14:05:37

29

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Evaluating a derived functor on an object where the original functor is 0

Published on 04 Nov 2023 - 14:05

score 57 · Answer 3 · 2026-03-26 03:06:10

57

Views

Can we explicitly describe the derived pullback $\mathbf L\pi^* \widetilde M$ for a closed immersion $\pi$ of affine schemes?

Published on 26 Mar 2026 - 3:06

score 37 · Answer 4 · 2026-03-25 03:24:07

37

Views

$2$ part of $Ext(\Bbb{Z}/2\Bbb{Z}, A)$ when $A$ is finite

Published on 25 Mar 2026 - 3:24

score 328 · Answer 5 · 2023-11-29 16:41:34

328

Views

Suppose $0\to A\to B\to C\to D\to 0$ is exact. Let $0\to A[2]\to B[2]\to C[2]\to X\to 0$ be an exact sequence. Then, $X [2]$ is finite.

Published on 29 Nov 2023 - 16:41

score 67 · Answer 6 · 2023-12-04 17:58:01

67

Views

Topological proof that $Ext(A, \mathbb{Q})=0$

Published on 04 Dec 2023 - 17:58

score 176 · Answer 7 · 2023-12-07 23:11:03

176

Views

$\mathrm{Ext}$ and direct limit

Published on 07 Dec 2023 - 23:11

score 59 · Answer 8 · 2023-12-11 18:39:26

59

Views

Show $E \cong E'$ as R-modules given $ h : N \to N'$ isomorphism, $\mathscr E : 0 \to N \to E \to M \to 0$ and its pushout

Published on 11 Dec 2023 - 18:39

score 40 · Answer 9 · 2024-01-05 17:43:34

40

Views

Can the inflation map be seen as a map between two $\delta$-functors?

Published on 05 Jan 2024 - 17:43

score 50 · Answer 10 · 2024-01-23 12:59:45

50

Views

A faulty "proof" regarding exactness of derived functors

Published on 23 Jan 2024 - 12:59

score 63 · Answer 11 · 2024-01-30 14:36:13

63

Views

Basic questions of triangulated functors

Published on 30 Jan 2024 - 14:36

score 545 · Answer 12 · 2024-02-17 12:48:18

545

Views

What is the "goal" of derived functors?

Published on 17 Feb 2024 - 12:48

score 100 · Answer 13 · 2026-03-25 15:29:48

100

Views

On the two definitions of derived functor in general triangulated category.

Published on 25 Mar 2026 - 15:29

score 91 · Answer 14 · 2026-02-23 11:33:08

91

Views

Normality and integrality of schemes and splitting of map from structure sheaf to derived-pushforward of structure sheaf along proper birational map

Published on 23 Feb 2026 - 11:33

score 43 · Answer 15 · 2024-03-18 10:09:05

43

Views

Functoriality of derived tensor product ( Gortz's Algebraic Geometry, Vol.2. )

Published on 18 Mar 2024 - 10:09

List Question

Example of a factorisation of functors $F = HK$ for which the Kan extension of $F$ along $K$ is not $H$.

Evaluating a derived functor on an object where the original functor is 0

Can we explicitly describe the derived pullback $\mathbf L\pi^* \widetilde M$ for a closed immersion $\pi$ of affine schemes?

$2$ part of $Ext(\Bbb{Z}/2\Bbb{Z}, A)$ when $A$ is finite

Suppose $0\to A\to B\to C\to D\to 0$ is exact. Let $0\to A[2]\to B[2]\to C[2]\to X\to 0$ be an exact sequence. Then, $X [2]$ is finite.

Topological proof that $Ext(A, \mathbb{Q})=0$

$\mathrm{Ext}$ and direct limit

Show $E \cong E'$ as R-modules given $ h : N \to N'$ isomorphism, $\mathscr E : 0 \to N \to E \to M \to 0$ and its pushout

Can the inflation map be seen as a map between two $\delta$-functors?

A faulty "proof" regarding exactness of derived functors

Basic questions of triangulated functors

What is the "goal" of derived functors?

On the two definitions of derived functor in general triangulated category.

Normality and integrality of schemes and splitting of map from structure sheaf to derived-pushforward of structure sheaf along proper birational map

Functoriality of derived tensor product ( Gortz's Algebraic Geometry, Vol.2. )

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