List questions from diagram-chasing

Published on 25 Mar 2026 - 3:41

484

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Short five lemma and a counterexample: commutative diagram

Published on 01 Jul 2021 - 20:32

129

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If three functions in commutative diagram are bijection, is the fourth one too?

Published on 08 Aug 2021 - 10:37

326

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Why does the inner square commute if all outer squares commute?

Published on 08 Aug 2021 - 11:07

303

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How does a pushout and an exact sequence of modules give another exact sequence?

Published on 10 Aug 2021 - 19:20

60

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If $n$ is even $\exists [f] \in \pi_{2n-1}(\mathbb{S}^n)$ such that $H(f) = \pm 2$

Published on 13 Aug 2021 - 10:51

155

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What is the $\textbf{Set}$-theoretical intuition behind understanding how power objects work in Topos Theory?

Published on 09 Jan 2022 - 23:05

116

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Showing an induced sequence is exact.

Published on 10 Jan 2022 - 12:29

86

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$F$ left adjoint to $G \iff F,G$ define a functor from $\textbf{Arr}(\textbf{X}\times\textbf{A}) \to 2\times 1$ square CDs in $\textbf{Set}$?

Published on 25 Mar 2026 - 6:29

97

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If $E$ has pullbacks then $\text{SplitEpi}(E)$ has pullbacks

Published on 18 Feb 2022 - 17:21

168

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Prove that if $\alpha_{3}$ is an isomorphism, then the sequence is a short exact sequence.

Published on 07 Mar 2022 - 21:08

58

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Star-autonomous categories are linearly distributive categories with negation?

Published on 10 Apr 2022 - 10:11

146

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Coherence in closed monoidal categories

Published on 24 May 2022 - 14:15

228

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direct sum of two exact sequence is exact

Published on 29 May 2022 - 16:11

88

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Basic example in diagram chasing

Published on 19 Jun 2022 - 17:14

List Question

A colimit in a subcategory

Short five lemma and a counterexample: commutative diagram

If three functions in commutative diagram are bijection, is the fourth one too?

Why does the inner square commute if all outer squares commute?

How does a pushout and an exact sequence of modules give another exact sequence?

If $n$ is even $\exists [f] \in \pi_{2n-1}(\mathbb{S}^n)$ such that $H(f) = \pm 2$

What is the $\textbf{Set}$-theoretical intuition behind understanding how power objects work in Topos Theory?

Showing an induced sequence is exact.

$F$ left adjoint to $G \iff F,G$ define a functor from $\textbf{Arr}(\textbf{X}\times\textbf{A}) \to 2\times 1$ square CDs in $\textbf{Set}$?

If $E$ has pullbacks then $\text{SplitEpi}(E)$ has pullbacks

Prove that if $\alpha_{3}$ is an isomorphism, then the sequence is a short exact sequence.

Star-autonomous categories are linearly distributive categories with negation?

Coherence in closed monoidal categories

direct sum of two exact sequence is exact

Basic example in diagram chasing

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