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I read that Cayley's theorem can be extended to categories, i.e. that any category with a set of morphisms can be represented as a category with sets as objects and functions as morphisms. I was looking at the construction and for some reason I don't fully understand how they define the morphisms in the 'dual' category. If someone could please shed some light on this, I would appreciate it. But please don't post the whole proof of the representation result - I would like to try it out myself first.

Many thanks in advance!

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# Categorical extension of Cayley's Theorem

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