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Questions tagged [hom-functor]

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

Let $\Delta$ be the simplicial category. Let $\tilde{\Delta}$ be the subcategory of non-empty totally ordered sets as objects and order-preserving maps that also preserve the smallest and largest ...
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Hom-like functor to a topos other than Set?

The hom-set functor is often given as the bifunctor: $$ \mathbf{Hom}(-,-) : \cal C^{op} \times \cal C \to \mathbf{Set}$$ (This is of course under the assumption that $\cal C$ is locally small.) Is ...
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Does an adjoint of an internal Hom functor of a prounital closed category define a tensor product?

A closed category is a category equipped with internal Hom functors along with a unit object. Now this answer shows that if $C$ is a closed category whose internal Hom functor has a left adjoint, ...
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Nearly locally presentable categories

Here1, in the remark $2.3 (1)$ how from the fact that ${\cal K}(A,-)$ does not preserve coproducts it follows that ${\cal K}(A,-)$ sends special $\lambda$-directed colimits to $\lambda$-directed ...
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Question on the map induced by hom-functor

Let $R$ be a commutative ring with unity and let $M$ be a finitely generated noetherian $R$-module. Suppose we are given an $R$-homomorphism: $$ \varphi: R^{(2)}\to R^{(2)} $$ Fixing a basis of $R^{(...
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decomposition of hom-functors in a self-enriched category

Let $\mathbb{C}$ be a self-enriched category (such as Set). The Functor $\mathbb{C}(X, \mathbb{C}(Y,\_))$ is the same than the composition of functors $\mathbb{C}(X,\_) \circ \mathbb{C}(Y,\_)$. In a ...