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jpvillaisaza committed May 22, 2014
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6 changes: 3 additions & 3 deletions monads.tex
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Expand Up @@ -214,10 +214,10 @@ \subsection{Monads}
described in Example \ref{ex:category-monoid}. Let $\mon{T} =
(\func{T}, \nat{\eta}, \nat{\mu})$ be a monad in a category
$\cat{C}$. The endofunctor $\func{T}$ is the set of elements of a
monoid $M = (\func{T}, \nat{\eta}, \nat{\mu})$. The multiplication
natural transformation, $\nat{\eta}$, is the associative binary
monoid $M = (\func{T}, \nat{\mu}, \nat{\eta})$. The multiplication
natural transformation, $\nat{\mu}$, is the associative binary
operation of the monoid, and it has an identity, the unit natural
transformation, $\nat{\mu}$. Thus, the diagram in Figure
transformation, $\nat{\eta}$. Thus, the diagram in Figure
\ref{fig:monad-associativity} is the associative law for the monad,
while the diagram in Figure \ref{fig:monad-unity} expresses the left
and right unit laws \parencite[138]{maclane-1998}.
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2 changes: 1 addition & 1 deletion naturals.tex
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Expand Up @@ -301,7 +301,7 @@ \section{Natural Transformations in Haskell}
\texthaskell{head} and \texthaskell{last} functions, which show that
proofs of naturality differ according to the definition, and the
\texthaskell{concat} function, which is one of the examples of
theorems from types in \parencite[349]{wadler-1989}
theorems from types in \parencite[349]{wadler-1989}.

\begin{example}
\label{ex:natural-identity-haskell}
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