List questions from limits-colimits

Published on 25 Mar 2026 - 6:03

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$F : I → C$ is a functor from a filtered category with any colimit. $ι : J → I$ is the embedding with $J$ cofinal. Then colim $F \cong$ colim($F ◦ ι$)

Published on 26 Mar 2026 - 23:10

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Dual Concept of a Well-Powered Category

Published on 26 Mar 2026 - 22:53

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2-pullbacks in 2-functor 2-categories

Published on 23 Feb 2026 - 18:40

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Representable ind-objects

Published on 24 Nov 2023 - 15:46

151

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On kernels and stalks of sheaves.

Published on 30 Nov 2023 - 9:18

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Properties of the Projective Limit (in $\textbf{Set}$)

Published on 26 Mar 2026 - 14:24

114

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Cartesian products in categories of subobjects

Published on 03 Dec 2023 - 23:07

177

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$\mathrm{Ext}$ and direct limit

Published on 26 Mar 2026 - 7:55

95

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Generalizing pullbacks

Published on 09 Dec 2023 - 22:04

60

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Reference for the alternative construction of the free cocompletion

Published on 10 Dec 2023 - 19:09

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Prove that the forgetful functor $U: \textbf{Ab} \to \textbf{Set}$ preserves all filtered colimits

Published on 23 Feb 2026 - 3:30

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Proof verification computing pushout (i.e. colimit) of the diagram $\langle x \rangle \hookrightarrow D_{2\cdot n}, \langle x \rangle \to 1, |x| = n$

Published on 11 Dec 2023 - 1:50

67

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Is the category of graded modules over a graded-commutative ring an AB5 category?

Published on 26 Mar 2026 - 11:47

87

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Coequalizer that is not absolute

Published on 12 Dec 2023 - 18:34

List Question

Fundamental groupoid of a filtered union

$F : I → C$ is a functor from a filtered category with any colimit. $ι : J → I$ is the embedding with $J$ cofinal. Then colim $F \cong$ colim($F ◦ ι$)

Dual Concept of a Well-Powered Category

2-pullbacks in 2-functor 2-categories

Representable ind-objects

On kernels and stalks of sheaves.

Properties of the Projective Limit (in $\textbf{Set}$)

Cartesian products in categories of subobjects

$\mathrm{Ext}$ and direct limit

Generalizing pullbacks

Reference for the alternative construction of the free cocompletion

Prove that the forgetful functor $U: \textbf{Ab} \to \textbf{Set}$ preserves all filtered colimits

Proof verification computing pushout (i.e. colimit) of the diagram $\langle x \rangle \hookrightarrow D_{2\cdot n}, \langle x \rangle \to 1, |x| = n$

Is the category of graded modules over a graded-commutative ring an AB5 category?

Coequalizer that is not absolute

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