Question

Corepresentable functor definition.

score 94 · Answer 1 · 2023-05-25 15:22:32

94

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Corepresentable functor definition.

Published on 25 May 2023 - 15:22

score 70 · Answer 2 · 2026-02-23 15:11:12

70

Views

Existence of a right adjoint functor of the inverse image via a morphism of schemes between the categories of quasi-coherent modules

Published on 23 Feb 2026 - 15:11

score 70 · Answer 3 · 2026-03-24 15:59:14

70

Views

Representable presheaves on the slice category

Published on 24 Mar 2026 - 15:59

score 29 · Answer 4 · 2026-03-25 04:37:40

29

Views

Representable morphisms of algebraic spaces

Published on 25 Mar 2026 - 4:37

score 113 · Answer 5 · 2023-10-09 05:09:48

113

Views

How do I show that the forgetful functor $F : \text {Grp} \rightarrow \text {Set} $ is co-representable?

Published on 09 Oct 2023 - 5:09

score 126 · Answer 6 · 2023-10-16 16:34:23

126

Views

Prove that the functor $P : \text{Set}^\text{op} → \text{Set}$ , $F(f)=f^{-1}:P(Y)\rightarrow P(X)$ for $f: X \rightarrow Y$ is representable

Published on 16 Oct 2023 - 16:34

score 42 · Answer 7 · 2023-10-29 06:49:45

42

Views

Condition that limit of a diagram $F$ exists if $\alpha: Mor(-,L) \to \lim Mor(X,F(i))$

Published on 29 Oct 2023 - 6:49

score 81 · Answer 8 · 2023-11-01 01:30:31

81

Views

Prove that any functor $F : \mathcal C \to \text{Sets}$ where $\mathcal C$ is small is a colimit of representable functors

Published on 01 Nov 2023 - 1:30

score 49 · Answer 9 · 2024-02-11 11:44:00

49

Views

Tiny objects in a power set

Published on 11 Feb 2024 - 11:44

score 2.8k · Answer 10 · 2013-05-14 22:35:31

2.8k

Views

Representable functors preserve limits.

Published on 14 May 2013 - 22:35

score 51 · Answer 11 · 2017-08-21 22:00:02

51

Views

"Cats & Sheaves" defines $C_A$ w.r.t $F : C \to C'$ for object $A \in C'$, but then doesn't define $C_F$...

Published on 21 Aug 2017 - 22:00

score 94 · Answer 12 · 2017-08-28 03:15:52

94

Views

The isomorphism $F \simeq h_C(X)$ determines $X$ how?

Published on 28 Aug 2017 - 3:15

score 99 · Answer 13 · 2026-03-25 03:24:06

99

Views

Is there only one isomorphism $h_C(X) \simeq h_C(Y)$ if it exists?

Published on 25 Mar 2026 - 3:24

score 129 · Answer 14 · 2017-08-29 06:57:35

129

Views

Representability of zariski functors on schemes over a base by gluing

Published on 29 Aug 2017 - 6:57

score 127 · Answer 15 · 2017-08-29 09:30:08

127

Views

Given the adjunction morphisms $\epsilon, \eta$, then $(\eta \circ L) \circ(L\circ \epsilon) = \text{id}_L$ is easy to check.

Published on 29 Aug 2017 - 9:30

List Question

Corepresentable functor definition.

Existence of a right adjoint functor of the inverse image via a morphism of schemes between the categories of quasi-coherent modules

Representable presheaves on the slice category

Representable morphisms of algebraic spaces

How do I show that the forgetful functor $F : \text {Grp} \rightarrow \text {Set} $ is co-representable?

Prove that the functor $P : \text{Set}^\text{op} → \text{Set}$ , $F(f)=f^{-1}:P(Y)\rightarrow P(X)$ for $f: X \rightarrow Y$ is representable

Condition that limit of a diagram $F$ exists if $\alpha: Mor(-,L) \to \lim Mor(X,F(i))$

Prove that any functor $F : \mathcal C \to \text{Sets}$ where $\mathcal C$ is small is a colimit of representable functors

Tiny objects in a power set

Representable functors preserve limits.

"Cats & Sheaves" defines $C_A$ w.r.t $F : C \to C'$ for object $A \in C'$, but then doesn't define $C_F$...

The isomorphism $F \simeq h_C(X)$ determines $X$ how?

Is there only one isomorphism $h_C(X) \simeq h_C(Y)$ if it exists?

Representability of zariski functors on schemes over a base by gluing

Given the adjunction morphisms $\epsilon, \eta$, then $(\eta \circ L) \circ(L\circ \epsilon) = \text{id}_L$ is easy to check.

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