List questions from category-theory

Published on 11 Apr 2026 - 5:19

191

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In $\mathbf{Sets}^\mathbf{Q}$, prove the subobject classifier $\Omega$ is given by $\Omega(q)=\{r\mid r\in\mathbf{R^+},r\ge q\}.$

Published on 25 Mar 2026 - 22:30

41

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$Et/X$ is closed under finite limits in $Top/X$.

Published on 12 Apr 2026 - 2:47

271

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Idempotent completion

Published on 05 Apr 2026 - 14:10

216

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What objects can be turned into a category?

Published on 16 Apr 2026 - 5:53

126

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Proving Proposition I.5.1 of Mac Lane and Moerdijk.

Published on 25 Mar 2026 - 22:25

752

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Adjoints are Kan extensions

Published on 10 Apr 2026 - 20:12

124

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An arrow is monic iff the square is a pullback

Published on 25 Mar 2026 - 23:51

525

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Preservation of weak pullback

Published on 09 Apr 2026 - 15:02

102

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What is the corresponding categorical notion to a non-functorial modality?

Published on 25 Mar 2026 - 14:23

562

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What lies behind the definitions of split monics and epics?

Published on 20 Apr 2026 - 12:06

69

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A variation of a codomain fibration

Published on 13 Apr 2026 - 7:54

93

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Filling a map $X\times\Lambda^n_k\rightarrow Y$ to a map $X\times\Delta^n\rightarrow Y$

Published on 15 Apr 2026 - 13:24

497

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Part of proof of Yoneda's Lemma from Vakil

Published on 26 Mar 2026 - 19:20

189

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Algebraic Geometric Analogue of Brown's Representability

Published on 25 Mar 2026 - 9:27

List Question

A tower of Cartesian Products is Cartesian

In $\mathbf{Sets}^\mathbf{Q}$, prove the subobject classifier $\Omega$ is given by $\Omega(q)=\{r\mid r\in\mathbf{R^+},r\ge q\}.$

$Et/X$ is closed under finite limits in $Top/X$.

Idempotent completion

What objects can be turned into a category?

Proving Proposition I.5.1 of Mac Lane and Moerdijk.

Adjoints are Kan extensions

An arrow is monic iff the square is a pullback

Preservation of weak pullback

What is the corresponding categorical notion to a non-functorial modality?

What lies behind the definitions of split monics and epics?

A variation of a codomain fibration

Filling a map $X\times\Lambda^n_k\rightarrow Y$ to a map $X\times\Delta^n\rightarrow Y$

Part of proof of Yoneda's Lemma from Vakil

Algebraic Geometric Analogue of Brown's Representability

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