Question

Showing that the diagonal functor $\Delta:\mathbb{C} \to \mathbb{C} \times \mathbb{C}$ having a right adjoint implies $\mathbb{C}$ having products.

score 77 · Answer 1 · 2024-01-12 14:03:36

77

Views

Showing that the diagonal functor $\Delta:\mathbb{C} \to \mathbb{C} \times \mathbb{C}$ having a right adjoint implies $\mathbb{C}$ having products.

Published on 12 Jan 2024 - 14:03

score 87 · Answer 2 · 2024-01-12 17:48:20

87

Views

To prove two functors are left and right adjoint

Published on 12 Jan 2024 - 17:48

score 65 · Answer 3 · 2026-03-25 04:41:34

65

Views

Left adjoint to forgetful functor from groups to groupoids, generalizing injective inclusions to free product of groups

Published on 25 Mar 2026 - 4:41

score 40 · Answer 4 · 2024-01-18 14:57:08

40

Views

Constructing a left adjoint to the restriction functor $U:\mathsf{C}^{\mathsf{J}}\to\mathsf{C}^{\operatorname{ob}\mathsf{J}}$

Published on 18 Jan 2024 - 14:57

score 81 · Answer 5 · 2024-01-25 01:24:09

81

Views

Prove that $F$ is left adjoint to $G$ iff $G$ is right adjoint to $F$.

Published on 25 Jan 2024 - 1:24

score 39 · Answer 6 · 2024-01-27 22:51:12

39

Views

Category Theory: Natural Isomorphism of Bifunctors vs Argumentwise Natural Isomorphism

Published on 27 Jan 2024 - 22:51

score 40 · Answer 7 · 2024-01-30 15:57:43

40

Views

Existence of periodic adjunctions

Published on 30 Jan 2024 - 15:57

score 103 · Answer 8 · 2026-03-25 19:04:38

103

Views

Adjunction between convex spaces and Lawvere metric spaces

Published on 25 Mar 2026 - 19:04

score 75 · Answer 9 · 2024-02-01 15:23:20

75

Views

Understanding the Difference Between Adjoint and Inverse Functors

Published on 01 Feb 2024 - 15:23

score 60 · Answer 10 · 2024-02-05 20:19:35

60

Views

Left adjoint of an embedding

Published on 05 Feb 2024 - 20:19

score 100 · Answer 11 · 2024-02-09 10:41:42

100

Views

Forgetful functor $Z(C)\rightarrow C$ has Left Adjoint

Published on 09 Feb 2024 - 10:41

score 62 · Answer 12 · 2026-03-25 08:00:46

62

Views

Why is $\mathcal{C}$ equivalent to $\mathcal{C}^{\text{op}}$ when $\mathcal{C}$ is a compact category?

Published on 25 Mar 2026 - 8:00

score 68 · Answer 13 · 2026-03-22 05:12:50

68

Views

Concrete functors with left adjoint

Published on 22 Mar 2026 - 5:12

score 55 · Answer 14 · 2026-03-25 03:21:26

55

Views

Why does duality of objects $A$, $A^\ast$ in a symmetric monoidal category imply an adjunction $(-) \otimes A \dashv (-) \otimes A^\ast$?

Published on 25 Mar 2026 - 3:21

score 152 · Answer 15 · 2024-02-16 13:30:33

152

Views

Intuition behind 'adjointness' of adjoint functor for a lay person

Published on 16 Feb 2024 - 13:30

List Question

Showing that the diagonal functor $\Delta:\mathbb{C} \to \mathbb{C} \times \mathbb{C}$ having a right adjoint implies $\mathbb{C}$ having products.

To prove two functors are left and right adjoint

Left adjoint to forgetful functor from groups to groupoids, generalizing injective inclusions to free product of groups

Constructing a left adjoint to the restriction functor $U:\mathsf{C}^{\mathsf{J}}\to\mathsf{C}^{\operatorname{ob}\mathsf{J}}$

Prove that $F$ is left adjoint to $G$ iff $G$ is right adjoint to $F$.

Category Theory: Natural Isomorphism of Bifunctors vs Argumentwise Natural Isomorphism

Existence of periodic adjunctions

Adjunction between convex spaces and Lawvere metric spaces

Understanding the Difference Between Adjoint and Inverse Functors

Left adjoint of an embedding

Forgetful functor $Z(C)\rightarrow C$ has Left Adjoint

Why is $\mathcal{C}$ equivalent to $\mathcal{C}^{\text{op}}$ when $\mathcal{C}$ is a compact category?

Concrete functors with left adjoint

Why does duality of objects $A$, $A^\ast$ in a symmetric monoidal category imply an adjunction $(-) \otimes A \dashv (-) \otimes A^\ast$?

Intuition behind 'adjointness' of adjoint functor for a lay person

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