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fix: equation labels
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Jlh18 committed Dec 4, 2024
1 parent c58d844 commit 822e1e6
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions blueprint/src/chapter/natural_model.tex
Original file line number Diff line number Diff line change
Expand Up @@ -301,7 +301,7 @@ \subsection{Identity types}
\arrow["{\Star{\rho}_{\Type}}"', from=2-1, to=2-2]
\end{tikzcd}
\begin{equation}
\label{diag:J_definition_diagram}
\label{eq:JDefinition1}
\end{equation}
\end{center}
Taking the pullback $T$ and the comparison map $\ep$ we have
Expand All @@ -321,7 +321,7 @@ \subsection{Identity types}
\arrow["{\Star{\rho}_{\Type}}"', from=3-2, to=3-3]
\end{tikzcd}
\begin{equation}
\label{diag:J_definition}
\label{eq:JDefinition2}
\end{equation}
\end{center}
Finally, we require a section $\J : T \to \Poly{q}{\Term}$ of $\ep$,
Expand Down Expand Up @@ -834,7 +834,7 @@ \subsection{Stability of the universe under type formers}
The left face of the outer cube is the composed diagonal pullback square from
\ref{diag:universe-identity-type-classifier-pullback-cube}.
The front face of the outer cube is the naturality square for $\Star{\rho}$ from
\ref{diag:J_definition}
\ref{eq:JDefinition2}
and similarly the back face is the naturality square for $\Star{\rho_{U}}$ from
\ref{diag:J_U_definition}.

Expand Down Expand Up @@ -1088,7 +1088,7 @@ \subsection{Extensional identity types and UIP}
\arrow["\Id"', from=2-1, to=2-2]
\end{tikzcd}\end{center}
Note that this means $\Star{\rho}$ is an isomorphism,
from which it follows that \ref{diag:J_definition_diagram} is also a pullback,
from which it follows that \ref{eq:JDefinition1} is also a pullback,
i.e. $\ep$ is an isomorphism.
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\begin{center}\begin{tikzcd}
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