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I am looking for examples of locally small categories where one can talk about Yoneda lemma and produce some interesting(personal choice) results.

One such example is :

Let $G$ be a group. We construct a category whose objects set is singleton and whose set of morphisms is the group $G$. Then, Yoneda lemma applied to this category gives Cayley's theorem.

Are there any other examples like this?

I am asking for a long list of examples.

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    Are you looking for a long list of particular instances of Yoneda lemma applied to various structures? I'm not entirely sure what you are after... – Ittay Weiss Jul 20 '17 at 14:14
  • @IttayWeiss yes, I am looking for a list of particular instances of Yoneda lemma applied o various structures –  Jul 20 '17 at 15:02
  • Duplicate of https://math.stackexchange.com/questions/656451/theorems-implied-by-yonedas-lemma ? – fosco Jul 20 '17 at 16:00
  • @FoscoLoregian that does not really answer my question. One answer is Cayley's theorem that I have already mentioned others are just explanations of theorem and nothing specific. My question was to get a collection of theorems where you fix one locally small category, a Functor and then deduce some result from Yoneda lemma –  Jul 20 '17 at 16:20
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    I do not see how is this too broad. I am asking for a collection of examples –  Jul 21 '17 at 16:59
  • True, but you're asking for examples of an extremely broad class of mathematical objects. Further, it's hard to see what might make for an authoritative answer to this question. – Malice Vidrine Jul 21 '17 at 23:08
  • @MaliceVidrine can it be then made a community wiki?? –  Jul 24 '17 at 03:23
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    Here is an example: A ring $R$ can be seen as an additive category with one object. A module $M$ can be seen as a functor $M:R \rightarrow Ab$. Applying Yonneda yields the familiar isomorphism at the level of abelian groups : $Hom(R,M) \simeq M$ – Mike Jul 26 '17 at 07:58

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