List questions from hom-functor

Published on 22 Mar 2026 - 18:01

134

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Existence of morphisms in a free completion under directed colimits,$\lambda$-accessible category

Published on 23 Mar 2026 - 13:44

207

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Preservation of limits by representable functors

Published on 22 Mar 2026 - 19:52

122

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There is a natural morphism $\lim\limits_{\longleftarrow} \beta \to \lim\limits_{\longleftarrow} \beta \circ \varphi^{op}$?

Published on 22 Mar 2026 - 6:21

103

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Fully faithful nerve ⟹ injective on objects?

Published on 22 Mar 2026 - 15:28

350

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$\operatorname{Hom}$ functor is projective?

Published on 22 Mar 2026 - 14:22

111

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Nearly locally presentable categories

Published on 22 Mar 2026 - 4:46

624

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Existence of injective homomorphism

Published on 22 Mar 2026 - 11:19

258

Views

Isomorphism between Hom-space and $k$

Published on 22 Mar 2026 - 12:38

1.2k

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Is “monoidal category enriched over itself” the same as “closed monoidal category”?

Published on 21 Mar 2026 - 17:19

102

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Does an adjoint of an internal Hom functor of a prounital closed category define a tensor product?

Published on 17 Mar 2026 - 0:44

76

Views

Currying in a locally small category with coproducts

Published on 16 Mar 2026 - 22:53

80

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decomposition of hom-functors in a self-enriched category

Published on 21 Mar 2026 - 18:13

41

Views

How to see that $S(\sigma) = \text{Hom}_{\Delta}(\sigma, [0,1])$ maps to the category $\tilde{\Delta}^{\text{op}}$.

Published on 22 Mar 2026 - 14:13

136

Views

The Yoneda lemma and a natural bijection

Published on 22 Mar 2026 - 11:43

List Question

When can functors fail to be adjoints if their hom sets are bijective?

Existence of morphisms in a free completion under directed colimits,$\lambda$-accessible category

Preservation of limits by representable functors

There is a natural morphism $\lim\limits_{\longleftarrow} \beta \to \lim\limits_{\longleftarrow} \beta \circ \varphi^{op}$?

Fully faithful nerve ⟹ injective on objects?

$\operatorname{Hom}$ functor is projective?

Nearly locally presentable categories

Existence of injective homomorphism

Isomorphism between Hom-space and $k$

Is “monoidal category enriched over itself” the same as “closed monoidal category”?

Does an adjoint of an internal Hom functor of a prounital closed category define a tensor product?

Currying in a locally small category with coproducts

decomposition of hom-functors in a self-enriched category

How to see that $S(\sigma) = \text{Hom}_{\Delta}(\sigma, [0,1])$ maps to the category $\tilde{\Delta}^{\text{op}}$.

The Yoneda lemma and a natural bijection

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