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Update representable-functors.tex

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Bartosz Milewski 2020-03-27 08:46:31 -07:00
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@ -202,8 +202,8 @@ It must respect naturality conditions, and it must be the inverse of \code{alpha
alpha . beta = id = beta . alpha
\end{snip}
We will see later that a natural transformation from $\cat{C}(a, -)$
to any $\Set$-valued functor always exists (Yoneda's lemma) but it
is not necessarily invertible.
to any $\Set$-valued functor always exists as long as $F a$ is
non-empty (Yoneda's lemma) but it is not necessarily invertible.
Let me give you an example in Haskell with the list functor and
\code{Int} as \code{a}. Here's a natural transformation that does