List questions from hom-functor

143

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Why is $\text{Hom}_{\text{Set}}(S, \text{lim} F) \simeq \text{lim } \text{Hom}_{\text{Set}}(S, F(\cdot))$?

Published on 25 Mar 2026 - 5:07

1.6k

Views

Limits and $Hom(-,Y)$-functor in abelian categories

Published on 15 Apr 2026 - 10:36

64

Views

Homomorphism into a union of $R$-algebras.

Published on 13 Apr 2026 - 12:31

89

Views

coefficient ring for cohomology modules

Published on 14 Apr 2026 - 4:50

77

Views

Hom, H$^n$ and tensor product

Published on 11 Apr 2026 - 4:47

616

Views

Show that if $M$ is projective then $\operatorname{Hom}_R(M,.)$ is an exact functor.

Published on 16 Apr 2026 - 9:33

127

Views

Kernel of $\phi \colon $Hom$_R(\prod_{i \in I}A_i, B) \to \prod_{i \in I}\text{Hom}_R(A_i, B)$ is isomorphic to Hom$_R(\prod A_i/\sum^\oplus A_i, B)$.

Published on 15 Apr 2026 - 23:42

29

Views

Examples of not-full functors between two categories in both directions?

Published on 16 Apr 2026 - 12:55

96

Views

Injectivity of derived Hom functor base change map

Published on 14 Apr 2026 - 1:18

119

Views

Determine if a functor has right/left adjoint

Published on 10 Apr 2026 - 22:33

75

Views

How to refer to image of homset under a (not full, not faithful) functor.

Published on 12 Apr 2026 - 18:34

244

Views

Proof of derived tensor-hom adjunction

Published on 12 Apr 2026 - 20:59

716

Views

Proof verification: Yoneda preserves limits

Published on 25 Mar 2026 - 5:05

58

Views

Categories in which every object is a hom-object?

Published on 13 Apr 2026 - 10:40

207

Views

Definition of the cotensor in sSet

Published on 11 Apr 2026 - 8:02

List Question

Why is $\text{Hom}_{\text{Set}}(S, \text{lim} F) \simeq \text{lim } \text{Hom}_{\text{Set}}(S, F(\cdot))$?

Limits and $Hom(-,Y)$-functor in abelian categories

Homomorphism into a union of $R$-algebras.

coefficient ring for cohomology modules

Hom, H$^n$ and tensor product

Show that if $M$ is projective then $\operatorname{Hom}_R(M,.)$ is an exact functor.

Kernel of $\phi \colon $Hom$_R(\prod_{i \in I}A_i, B) \to \prod_{i \in I}\text{Hom}_R(A_i, B)$ is isomorphic to Hom$_R(\prod A_i/\sum^\oplus A_i, B)$.

Examples of not-full functors between two categories in both directions?

Injectivity of derived Hom functor base change map

Determine if a functor has right/left adjoint

How to refer to image of homset under a (not full, not faithful) functor.

Proof of derived tensor-hom adjunction

Proof verification: Yoneda preserves limits

Categories in which every object is a hom-object?

Definition of the cotensor in sSet

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