# Questions tagged [yoneda-lemma]

For questions related to Yoneda lemma in category theory, which *basically* says (among many other things it says) that every locally small category can be embedded nicely into it's functor category into the category of Sets. Use this tag along with (abstract-algebra) or (category-theory).

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### Yoneda lemma in a functor semicategory

I've read that the Yoneda lemma does not hold in general for semicategories (i.e., 'categories' possibly lacking identity morphisms)[1]. However, I'm wondering about a related situation, where there ...
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### Understanding the particle accelerator analogy for the Yoneda lemma

In his Algebraic Geometry class a few years back, Ravi Vakil explained Yoneda's lemma like this: You work at a particle accelerator. You want to understand some particle. All you can do are throw ...
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### Why naturality in Yoneda Lemma?

I understand the statement of Yoneda Lemma and its implications; however, at a very concrete level I have never seen how naturality condition is used in examples. Even when we consider a Yoneda ...
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### Proof that the Yoneda embedding is cartesian closed

Is there a reference somewhere that the Yoneda embedding is cartesian closed? I tried showing this myself, but after staring at it for an afternoon, I did not yet see a proof. I saw an answer here ...
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### Cats in context Lemma 2.4.7.

I'm failing to understand the argument behind Lemma 2.4.7. in page 86 from Emily Riehl's Category Theory in Context. In particular along the following reasoning: Here $\int F$ is the category of ...
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### Difficulty with converting Yoneda's natural isomorphy into a group isomorphism in the proof of Cayley's theorem

$\newcommand{\A}{\mathscr{A}}\newcommand{\Gc}{\mathscr{G}}\newcommand{\G}{\mathcal{G}}\newcommand{\s}{\mathsf{Set}}\newcommand{\op}{^{\mathsf{op}}}\newcommand{\sym}{\mathsf{Sym}}$I am having ...
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