by *Thorsten* on **September 5, 2008**.

Tagged as: Lunches.

I presented a simple derivation of Paul’s construction of the exponential of containers. I used the opportunity to discuss the exponential of functors and the Yoneda lemma. My derivation is based on the observation that writing for the exponentiation of functors and is a *Napieran functor*.

This can be shown using the Yoneda lemma. Then given a container and a functor we can reason as follows:

This shows that one can exponentiate any functor with a container (predicatively) and that exponent of containers is a container, since we know that is a container and containers are closed under composition and products. Expanding the definition gives rise to Paul’s definition.

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