List questions from hom-functor

Published on 29 Nov 2023 - 13:04

55

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Defining the presehaf Hom(-,U) as a sheaf

Published on 03 Dec 2023 - 13:01

110

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$H^n(X,G)$ is isomorphic to $\operatorname{Hom}(H_n(X), G),$ for any space $X$ or for any chain complex $\mathcal{C}$, yes or no.

Published on 19 Dec 2023 - 17:32

54

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

Published on 14 Feb 2024 - 15:47

504

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Hom functors preserve fibre products.

Published on 24 Mar 2026 - 21:39

116

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Yoneda lemma, wrong direction, weighted colimit

Published on 06 Aug 2017 - 12:23

121

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Yoneda Lemma (again)

Published on 23 Mar 2026 - 20:34

246

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How does $h_C(f) : h_C(X) \to h_C(Y)$ an isomorphism imply $f$ is (Yoneda Lemma)?

Published on 18 Aug 2017 - 22:36

547

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Representability $h_C(X) \simeq F$ of functors determines rep. $X$ up to unique isomorphism (using Yoneda Lemma).

Published on 19 Aug 2017 - 0:42

98

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

Published on 29 Aug 2017 - 0:35

169

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What does "$\text{Hom}(\space, G)$takes values in Groups" mean?

Published on 25 Sep 2017 - 14:10

69

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Hom-like functor to a topos other than Set?

Published on 27 Sep 2017 - 9:56

238

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Does a fully faithful functor apply to identity arrows?

Published on 01 Oct 2017 - 18:05

5.5k

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Direct sum and Hom

Published on 22 Mar 2026 - 1:59

149

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Question on the map induced by hom-functor

Published on 27 Nov 2017 - 14:38

List Question

$2$ part of $Ext(\Bbb{Z}/2\Bbb{Z}, A)$ when $A$ is finite

Defining the presehaf Hom(-,U) as a sheaf

$H^n(X,G)$ is isomorphic to $\operatorname{Hom}(H_n(X), G),$ for any space $X$ or for any chain complex $\mathcal{C}$, yes or no.

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

Hom functors preserve fibre products.

Yoneda lemma, wrong direction, weighted colimit

Yoneda Lemma (again)

How does $h_C(f) : h_C(X) \to h_C(Y)$ an isomorphism imply $f$ is (Yoneda Lemma)?

Representability $h_C(X) \simeq F$ of functors determines rep. $X$ up to unique isomorphism (using Yoneda Lemma).

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

What does "$\text{Hom}(\space, G)$takes values in Groups" mean?

Hom-like functor to a topos other than Set?

Does a fully faithful functor apply to identity arrows?

Direct sum and Hom

Question on the map induced by hom-functor

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