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I just watched an introductory lecture to the concept of "adjunctions" in category theory, and read an introductory text on it. They explained the definition, some examples, and how to work with them.

But I still find the concept a bit elusive. What is the intuitive concept that is captured by a statement like "the product is the left adjunct of the exponential"?

Arnaud D.
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user56834
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    To me, the most canonical example of an adjunction is between the underlying set functor $U : \mathbf{Groups} \to \mathbf{Sets}$ and the free group functor $F : \mathbf{Sets} \to \mathbf{Groups}$. It might help to concentrate more on this example than on the product/exponential adjunction. – Daniel Schepler Feb 04 '19 at 19:44
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    I agree with Daniel's comment : if you have an intuition for free groups or free abelian groups; or even free algebraic structures of any kind, this intuition can guide you to understand adjunctions. – Maxime Ramzi Feb 04 '19 at 20:17
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    You can take a look at this question, or this one, or this one, or this one. – Arnaud D. Feb 04 '19 at 20:24

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