List questions from adjoint-functors

Published on 23 Oct 2023 - 20:12

65

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Proving bijectivity of the isomorphism when finding the right adjoint of functor F: Haus $\rightarrow$ to Top

Published on 23 Oct 2023 - 23:15

63

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Is $p^{-1}\mathcal F = p^!\mathcal F$ if $p: Y \to X$ is a covering map?

Published on 31 Oct 2023 - 8:47

53

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Condition for a symmetric monoidal category to be closed

Published on 04 Nov 2023 - 15:41

80

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'Uniqueness' of adjoint functors

Published on 25 Mar 2026 - 15:39

85

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On the adjointness of the inclusion and the zero-homology functor

Published on 10 Nov 2023 - 13:10

55

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Proving the existance and uniqueness of the unit of an adjunction

Published on 25 Mar 2026 - 15:42

48

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$F : C \to D$ is an equivalence of categories with quasi-inverse $G: D \to C$. Does the pair $(F,G)$ necessarily form an adjunction?

Published on 14 Nov 2023 - 5:59

34

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Dual Concept of a Well-Powered Category

Published on 15 Nov 2023 - 10:41

114

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Proving naturality in both arguments

Published on 25 Mar 2026 - 15:39

36

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Left and right exactness of adjoint functors

Published on 09 Dec 2023 - 20:37

53

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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

33

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Two-variable adjunction

Published on 17 Dec 2023 - 16:17

73

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Examples of adjoint 2-functors

Published on 24 Dec 2023 - 5:21

87

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Left and right adjoints of functor category inclusion

Published on 26 Mar 2026 - 7:14

List Question

inclusion functor Haus $\rightarrow$ Top does not have a right adjoint

Proving bijectivity of the isomorphism when finding the right adjoint of functor F: Haus $\rightarrow$ to Top

Is $p^{-1}\mathcal F = p^!\mathcal F$ if $p: Y \to X$ is a covering map?

Condition for a symmetric monoidal category to be closed

'Uniqueness' of adjoint functors

On the adjointness of the inclusion and the zero-homology functor

Proving the existance and uniqueness of the unit of an adjunction

$F : C \to D$ is an equivalence of categories with quasi-inverse $G: D \to C$. Does the pair $(F,G)$ necessarily form an adjunction?

Dual Concept of a Well-Powered Category

Proving naturality in both arguments

Left and right exactness of adjoint functors

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

Two-variable adjunction

Examples of adjoint 2-functors

Left and right adjoints of functor category inclusion

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