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UlrikBuchholtz committed Oct 1, 2024
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Expand Up @@ -690,13 +690,13 @@ \subsection{Higher deloopings}
equivalence $(TX, t) \ptdweto X$.
\end{proof}

\begin{exercise}\label{xca:sections-as-dependent-functions}
Recall that a {\em section} (see~\cref{def:surjection} and its
\begin{xca}\label{xca:sections-as-dependent-functions}
Recall that a \emph{section} (see~\cref{def:surjection} and its
accompanying footnote) of a function $f:A \to B$ is a function
$s: B \to A$ together with an identification $f\circ s \eqto \id_B$.
Construct an equivalence from the type $\secfun f$ of sections of
$f$ to the type $\prod_{b:B}\sum_{a:A}b \eqto f(a)$.
\end{exercise}
\end{xca}

Consider the evaluation function
$\ev_{X_\div,Y} : (X_\div \eqto Y) \to Y$ (defined by path-induction,
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