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EFanZh 2024-06-24 19:18:29 +09:00 committed by GitHub
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3 changed files with 3 additions and 3 deletions

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@ -68,7 +68,7 @@ and $G f$ in $\cat{D}$:
G f \Colon G a \to G b
\end{gather*}
The natural transformation $\alpha$ provides two additional morphisms
that complete the diagram in \emph{D}:
that complete the diagram in $\cat{D}$:
\begin{gather*}
\alpha_a \Colon F a \to G a \\

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@ -299,7 +299,7 @@ explore alternative implementations that have practical value.
\begin{enumerate}
\tightlist
\item
Show that the hom-functors map identity morphisms in \emph{C} to
Show that the hom-functors map identity morphisms in $\cat{C}$ to
corresponding identity functions in $\Set$.
\item
Show that \code{Maybe} is not representable.

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@ -98,7 +98,7 @@ These conditions, too, may be replaced by naturality. You may recall
that the \emph{universal} cone, or the limit, is defined as a natural
transformation between the (contravariant) hom-functor:
\[F \Colon c \to \cat{C}(c, \Lim[D])\]
and the (also contravariant) functor that maps objects in \emph{C} to
and the (also contravariant) functor that maps objects in $\cat{C}$ to
cones, which themselves are natural transformations:
\[G \Colon c \to \cat{Nat}(\Delta_c, D)\]
Here, $\Delta_c$ is the constant functor, and $D$ is the functor