The yoneda-lemma tag has no wiki summary.

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### In what generality does Eilenberg-Watts hold?

In homological algebra, the Eilenberg-Watts theorem states that if $F\colon\text{Mod}_R\to\text{Mod}_S$ is a right-exact coproduct preserving functor of modules, then $F\cong-\otimes_R F(R).$ The ...

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### Yoneda on a not so small category

I am working with "usual" category theory, maybe over ZFC, and I have a functor $F : Set \to Set$. I'd like to apply Yoneda lemma to $F$, i.e. obtain:
$$ [Set, Set](h_A, F) \cong F A $$
However, ...

**4**

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**1**answer

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### Unicity of Yoneda isomorphism

I am wondering if there is only one unique Yoneda isomorphism, that is a natural isomorphism (natural in C and P, that is) between Hom(yC,P) and PC.
The Yoneda lemma says that there exists at least ...

**5**

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**1**answer

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### Subcategories which still give a Yoneda embedding

If $\mathbf{C}$ is a category, then the Yoneda functor which sends $a$ to $Hom_\mathbf{C}(-,a)$ is a fully faithful embedding of categories
$$ \mathbf{C}\rightarrow ...

**9**

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**1**answer

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### Given a small category with some colimits, can the rest of the colimits be added?

Let $\mathcal{A}$ be a small category with some ( maybe no) colimits. What I would like to be able to do is add the rest of the colimits in a universal way. The Yoneda lemma will not work, since this ...

**2**

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**1**answer

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### Reference Request(Enriched Categories): Metric on Lipschitz Continuous Functions

If we consider metric spaces to be categories enriched over $\mathbb R_{\geq 0}$, the object corresponding to presheaves should be lipschitz-continuous functions $\operatorname{Lip^ 1}(M, \mathbb ...