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@ -68,7 +68,7 @@ and $G f$ in $\cat{D}$:
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G f \Colon G a \to G b
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\end{gather*}
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The natural transformation $\alpha$ provides two additional morphisms
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that complete the diagram in \emph{D}:
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that complete the diagram in $\cat{D}$:
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\begin{gather*}
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\alpha_a \Colon F a \to G a \\
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@ -299,7 +299,7 @@ explore alternative implementations that have practical value.
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\begin{enumerate}
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\tightlist
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\item
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Show that the hom-functors map identity morphisms in \emph{C} to
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Show that the hom-functors map identity morphisms in $\cat{C}$ to
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corresponding identity functions in $\Set$.
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\item
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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
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that the \emph{universal} cone, or the limit, is defined as a natural
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transformation between the (contravariant) hom-functor:
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\[F \Colon c \to \cat{C}(c, \Lim[D])\]
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and the (also contravariant) functor that maps objects in \emph{C} to
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and the (also contravariant) functor that maps objects in $\cat{C}$ to
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cones, which themselves are natural transformations:
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\[G \Colon c \to \cat{Nat}(\Delta_c, D)\]
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Here, $\Delta_c$ is the constant functor, and $D$ is the functor
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