Question

Naturality of the ker-coker sequence of snake lemma in an abelian category

score 408 · Answer 1 · 2026-03-24 17:22:44

408

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Naturality of the ker-coker sequence of snake lemma in an abelian category

Published on 24 Mar 2026 - 17:22

score 86 · Answer 2 · 2020-04-18 20:21:03

86

Views

Creation of limits and diagram chasing

Published on 18 Apr 2020 - 20:21

score 88 · Answer 3 · 2020-04-19 19:06:26

88

Views

Doubt on a particular commutative diagram using the Tensor Product construction

Published on 19 Apr 2020 - 19:06

score 108 · Answer 4 · 2020-04-26 15:31:21

108

Views

How should I proceed with diagram chasing in this commutative diagram?

Published on 26 Apr 2020 - 15:31

score 150 · Answer 5 · 2026-03-23 13:36:02

150

Views

Category with multiple classes/types/labelled morphisms?

Published on 23 Mar 2026 - 13:36

score 174 · Answer 6 · 2020-05-04 01:05:57

174

Views

$a \times \mathbf 1 \cong a$ in categories admitting products and having a terminal object $\mathbf 1$

Published on 04 May 2020 - 1:05

score 120 · Answer 7 · 2020-05-17 19:21:20

120

Views

Suppose that $g$ is isomorphism. Then prove that $f$ is monic and $h$ is epic.

Published on 17 May 2020 - 19:21

score 375 · Answer 8 · 2026-02-23 04:47:06

375

Views

any cofibration $i:A \to B$ is a homeomorphism onto its image (question regarding the inverse map)

Published on 23 Feb 2026 - 4:47

score 36 · Answer 9 · 2020-06-07 12:34:02

36

Views

Proving simplicial homology is preserved on mapping?

Published on 07 Jun 2020 - 12:34

score 70 · Answer 10 · 2020-06-14 21:26:05

70

Views

Show that $\ker\sigma \subset \varphi_1(\ker\rho)$ and $\operatorname{im}\tau \subset \psi_2(\operatorname{im}\sigma)$.

Published on 14 Jun 2020 - 21:26

score 54 · Answer 11 · 2020-06-22 16:13:50

54

Views

Two homomorphisms $f\colon A\to A',\ g\colon B\to B'$ induce a homomorphism $f \otimes g: A\otimes B \to A'\otimes B'$

Published on 22 Jun 2020 - 16:13

score 216 · Answer 12 · 2026-03-24 11:48:07

216

Views

What is a clear, elegant proof that $\text{Hom}(\cdot, Y)$ is a right-exact functor in a category of modules?

Published on 24 Mar 2026 - 11:48

score 69 · Answer 13 · 2020-07-23 10:18:03

69

Views

Can one obtain from the following diagram that the map $f_3$ is injective?

Published on 23 Jul 2020 - 10:18

score 90 · Answer 14 · 2016-08-13 13:08:58

90

Views

Equaliser of homomorphism of integers

Published on 13 Aug 2016 - 13:08

score 566 · Answer 15 · 2016-10-08 14:41:59

566

Views

Diagram chasing in Abelian categories?

Published on 08 Oct 2016 - 14:41

List Question

Naturality of the ker-coker sequence of snake lemma in an abelian category

Creation of limits and diagram chasing

Doubt on a particular commutative diagram using the Tensor Product construction

How should I proceed with diagram chasing in this commutative diagram?

Category with multiple classes/types/labelled morphisms?

$a \times \mathbf 1 \cong a$ in categories admitting products and having a terminal object $\mathbf 1$

Suppose that $g$ is isomorphism. Then prove that $f$ is monic and $h$ is epic.

any cofibration $i:A \to B$ is a homeomorphism onto its image (question regarding the inverse map)

Proving simplicial homology is preserved on mapping?

Show that $\ker\sigma \subset \varphi_1(\ker\rho)$ and $\operatorname{im}\tau \subset \psi_2(\operatorname{im}\sigma)$.

Two homomorphisms $f\colon A\to A',\ g\colon B\to B'$ induce a homomorphism $f \otimes g: A\otimes B \to A'\otimes B'$

What is a clear, elegant proof that $\text{Hom}(\cdot, Y)$ is a right-exact functor in a category of modules?

Can one obtain from the following diagram that the map $f_3$ is injective?

Equaliser of homomorphism of integers

Diagram chasing in Abelian categories?

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