Question

Defining $\text{Ker }f\xrightarrow{j}A,\text{Im }f\xrightarrow{k} B,p:\text{Ker }c\to \text{Ker }f,q:\text{Im }c\to \text{Im }f,$ using elements?

score 67 · Answer 1 · 2026-04-15 19:18:25

67

Views

Defining $\text{Ker }f\xrightarrow{j}A,\text{Im }f\xrightarrow{k} B,p:\text{Ker }c\to \text{Ker }f,q:\text{Im }c\to \text{Im }f,$ using elements?

Published on 15 Apr 2026 - 19:18

score 44 · Answer 2 · 2026-04-13 07:39:35

44

Views

Defining linear transformation: $r:\text{Coker }b \to \text{Coker }c.$ given a commutative sqaure diagram.

Published on 13 Apr 2026 - 7:39

score 53 · Answer 3 · 2026-04-14 08:10:22

53

Views

Commutative square inducing a linear transformation $r:\text{Coker }b\to \text{Coker }c.$

Published on 14 Apr 2026 - 8:10

score 31 · Answer 4 · 2026-04-16 11:30:58

31

Views

Meaning of: any exact sequence'can be recovered by "composing" the short exact sequences...

Published on 16 Apr 2026 - 11:30

score 116 · Answer 5 · 2026-04-12 05:02:21

116

Views

Given $\varphi:A\to B$, how do I describe the following six maps in terms of elements?

Published on 12 Apr 2026 - 5:02

score 24 · Answer 6 · 2026-04-17 09:37:02

24

Views

Meaning of: "$M'$ is the kernel of the canonical surjective morphism" and "$\text{Im} f$ is the kernel of $\text{Coker }f$?"

Published on 17 Apr 2026 - 9:37

score 64 · Answer 7 · 2026-04-11 04:13:05

64

Views

how to understand the meaning of kernel, cokernel, coimage, etc of another morphism.

Published on 11 Apr 2026 - 4:13

score 81 · Answer 8 · 2026-04-14 14:47:50

Clarifications need for passages explaining about cokernel, kernel, image and co-image in Cohn's $\textit{Further Algebra with Applications}$ text

score 39 · Answer 9 · 2026-04-11 02:06:29

39

Views

Clarifications need for confusing passage about kernel in Cohn's $\textit{Further Algebra with Applications}$ text

Published on 11 Apr 2026 - 2:06

score 25 · Answer 10 · 2026-04-11 22:48:20

25

Views

Clarifications need for unclear notations in passage from Cohn's $\textit{Further Algebra with Applications}$ text

Published on 11 Apr 2026 - 22:48

score 122 · Answer 11 · 2026-04-12 05:28:53

122

Views

Inverse morphism of group object is iso

Published on 12 Apr 2026 - 5:28

score 70 · Answer 12 · 2026-04-14 04:08:12

How is defined a domain (/codomain) in Category Theory? As a function, it is a morphism hence has a domain (/codomain). This, infinitely?

score 64 · Answer 13 · 2026-05-11 05:07:51

How does the following commutative diagram within the following proof match the definition for universal property of the kernel and also what is $g?$

score 49 · Answer 14 · 2026-04-14 05:17:34

49

Views

Are both $g', g$ assumed to be surjective in the commutative diagram for $3 \times 3$ lemma?

Published on 14 Apr 2026 - 5:17

score 34 · Answer 15 · 2026-04-13 20:35:53

34

Views

Why the need to show well definedness for the following case of restriction maps?

Published on 13 Apr 2026 - 20:35

List Question

Defining $\text{Ker }f\xrightarrow{j}A,\text{Im }f\xrightarrow{k} B,p:\text{Ker }c\to \text{Ker }f,q:\text{Im }c\to \text{Im }f,$ using elements?

Defining linear transformation: $r:\text{Coker }b \to \text{Coker }c.$ given a commutative sqaure diagram.

Commutative square inducing a linear transformation $r:\text{Coker }b\to \text{Coker }c.$

Meaning of: any exact sequence'can be recovered by "composing" the short exact sequences...

Given $\varphi:A\to B$, how do I describe the following six maps in terms of elements?

Meaning of: "$M'$ is the kernel of the canonical surjective morphism" and "$\text{Im} f$ is the kernel of $\text{Coker }f$?"

how to understand the meaning of kernel, cokernel, coimage, etc of another morphism.

Clarifications need for passages explaining about cokernel, kernel, image and co-image in Cohn's $\textit{Further Algebra with Applications}$ text

Clarifications need for confusing passage about kernel in Cohn's $\textit{Further Algebra with Applications}$ text

Clarifications need for unclear notations in passage from Cohn's $\textit{Further Algebra with Applications}$ text

Inverse morphism of group object is iso

How is defined a domain (/codomain) in Category Theory? As a function, it is a morphism hence has a domain (/codomain). This, infinitely?

How does the following commutative diagram within the following proof match the definition for universal property of the kernel and also what is $g?$

Are both $g', g$ assumed to be surjective in the commutative diagram for $3 \times 3$ lemma?

Why the need to show well definedness for the following case of restriction maps?

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