List questions from hom-functor

142

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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 02 Dec 2017 - 17:53

1.6k

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

Published on 19 Dec 2017 - 21:28

61

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Homomorphism into a union of $R$-algebras.

Published on 23 Aug 2020 - 2:33

87

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coefficient ring for cohomology modules

Published on 28 Sep 2020 - 6:16

73

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Hom, H$^n$ and tensor product

Published on 18 Jan 2021 - 12:01

613

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

Published on 26 Feb 2021 - 5:24

124

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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 27 Mar 2021 - 20:02

26

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

Published on 11 May 2021 - 23:07

93

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Injectivity of derived Hom functor base change map

Published on 16 May 2021 - 10:32

116

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Determine if a functor has right/left adjoint

Published on 30 Jun 2021 - 16:57

72

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

Published on 11 Jul 2021 - 3:51

241

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Proof of derived tensor-hom adjunction

Published on 09 Aug 2021 - 12:49

715

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Proof verification: Yoneda preserves limits

Published on 06 Sep 2021 - 14:07

55

Views

Categories in which every object is a hom-object?

Published on 16 Sep 2021 - 3:08

204

Views

Definition of the cotensor in sSet

Published on 23 Nov 2021 - 14:53

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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